www.klassenarbeiten.de Seite 1
Einfache Gleichungen 1
a) x + 3 = 8 b) x + 2 = 12 c) x + 9 = 18
d) x + 4 = 5 e) x + 22 = 44 f) x + 28 = 301.
g) x + 7 = 2 h) x + 8 = –4 i) x + 2 = –12
a) x – 1 = 2 b) x – 3 = 5 c) x – 4 = 11
d) x – 8 = 9 e) x – 2 = 13 f) x – 12 = 222.
g) x – 7 = –11 h) x – 9 = –14 i) x – 1 = –19
a) x 5 15 ⋅ = b) x 2 8 ⋅ = c) x 7 21 ⋅ =
d) 3 x 27 ⋅ = e) 9 x 45 ⋅ = f) 8 x 64 ⋅ =
3.
g) x 2 4,2 ⋅ = h) 5 x 12,5 ⋅ = i) 9 x 1,8 ⋅ =
xa) 22 = xb) 15 = xc) 98 =
xd) 95 = xe) 77 = xf ) 9 6 =
4.
xg) 0,310 = xh) 1,14 = xi) 0,88 =
a) x – 2 = 5 b) 3 + x = 1
c)
x 412 = −
d) 3 x 3,6 ⋅ = e) x ( 4) 3,6 ⋅ − = − xf ) 1,1 3 = −
5.
g) x + 1,8 = 2,2 h) x – 3,6 = 1,5 i) 3 x 1,5 − ⋅ = −
a) 3 – x = 4 b) 2 – x = 8 c) 7 – x = 5
d) 9 – x = –3 e) 5 – x = – 8 f) –3 – x = –1 6.
g) –2 – x = 6 h) 3 – x = 5 i) –4 – x = 12
a) 3x + 4 = 16 b) 2x + 3 = 13 c) 4 + 5x = 19
d) 4x – 1 = 15 e) 9x – 8 = 19 f) 10x – 15 = 457.
g) 5 – 2x = 15 h) 3 – 6x = 21 i) 9 – 5x = –36
xa) 4 32 − = xb) 3 23+ = xc) 3 45 − =
xd) 8 25 + = xe) 4 58+ = 3xf ) 2 5 4 + =
8.
2xg) 1 55 − = 5xh) 4 16− + = 2xi) 9 119+ =
12a) 3x = 6b) 3x = 15c) 15x =9.
14d) 7x = 16e) 4x = 49f ) 7 x =
Einfache Gleichungen 1
a) x + 3 = 8 b) x + 2 = 12 c) x + 9 = 18
d) x + 4 = 5 e) x + 22 = 44 f) x + 28 = 301.
g) x + 7 = 2 h) x + 8 = –4 i) x + 2 = –12
a) x – 1 = 2 b) x – 3 = 5 c) x – 4 = 11
d) x – 8 = 9 e) x – 2 = 13 f) x – 12 = 222.
g) x – 7 = –11 h) x – 9 = –14 i) x – 1 = –19
a) x 5 15 ⋅ = b) x 2 8 ⋅ = c) x 7 21 ⋅ =
d) 3 x 27 ⋅ = e) 9 x 45 ⋅ = f) 8 x 64 ⋅ =
3.
g) x 2 4,2 ⋅ = h) 5 x 12,5 ⋅ = i) 9 x 1,8 ⋅ =
xa) 22 = xb) 15 = xc) 98 =
xd) 95 = xe) 77 = xf ) 9 6 =
4.
xg) 0,310 = xh) 1,14 = xi) 0,88 =
a) x – 2 = 5 b) 3 + x = 1
c)
x 412 = −
d) 3 x 3,6 ⋅ = e) x ( 4) 3,6 ⋅ − = − xf ) 1,1 3 = −
5.
g) x + 1,8 = 2,2 h) x – 3,6 = 1,5 i) 3 x 1,5 − ⋅ = −
a) 3 – x = 4 b) 2 – x = 8 c) 7 – x = 5
d) 9 – x = –3 e) 5 – x = – 8 f) –3 – x = –1 6.
g) –2 – x = 6 h) 3 – x = 5 i) –4 – x = 12
a) 3x + 4 = 16 b) 2x + 3 = 13 c) 4 + 5x = 19
d) 4x – 1 = 15 e) 9x – 8 = 19 f) 10x – 15 = 457.
g) 5 – 2x = 15 h) 3 – 6x = 21 i) 9 – 5x = –36
xa) 4 32 − = xb) 3 23+ = xc) 3 45 − =
xd) 8 25 + = xe) 4 58+ = 3xf ) 2 5 4 + =
8.
2xg) 1 55 − = 5xh) 4 16− + = 2xi) 9 119+ =
12a) 3x = 6b) 3x = 15c) 15x =9.
14d) 7x = 16e) 4x = 49f ) 7 x =
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Gleichungen mit Additions- und Subtraktionsklammern
a) 2x + (3x + 4) = 19 b) 12x + (3x + 4) + (2x + 3) = 41
c) 12x – 4 + (3x + 1) = 27 d) 8x – 3 + (x + 1) = 2x + 7 + (4x + 3)1.
e) 4 – (3x – 2) + 5x = 4 – (x + 1) f) (4x – 4) – 8 = –(3x – 2)
a) 12x + (13x – 19) – (11x – 15) = 25 – (17 – 13x)
b) (3x + 7) – 6 = 12x – (x + 4) – (4x – 5)
c) (5x – 3 ) – (2x – 4) = – (x + 3) – (x + 5) + (x + 3)
d) 12 – (5x + 8) – (8x – 12) = 14x – 25 – (3x – 8) + (7x + 2)
e) –(3x – 5) – (7x – 24) = 3 + (x + 1) – (2x – 7)
2.
f) 12x – (3x + 8) + (39 – 5x) = 14 + (25x – 8) – (41 – x)
a) 12x – 3 – (23x – 48) + (x + 93) = 58x – (24x – 44) + 6
b) –(19x + 51) – (11x + 4) = –(39x + 45) + (8x – 7) – 24
c) 24 – (14x – 8) – (3 + 12x) = 4 – (8x + 11)
d) 3,7 – (8,1x + 5,4) – (2,6x + 8,3) = –3,1x + (8 – 1,6x)
e) (4,5x + 56) – (2,25x – 7) – (300 – 3x) = – (0,75x – 3)
3.
f) 3,5x – 6 – (4 – 2x) = (2,4x – 9,4) – (1,2x – 25,2)
Gleichungen – Klammer mal Zahl
a) 7(x – 2) = 49 b) 7(5x + 2) + 9 = 58
c) 15(8x – 24) = 120 d) 6(3x – 25) = 121.
e) 12(5x – 2) = 48 + 12x f) 3(4x + 18) = 6x + 108
a) 23(2x + 5) = 6x + 315 b) 17(5x + 3) = 401 + 35x
c) 16(2x – 3) = 5(4x + 16) + 4 d) 12(8x – 25) = 5(16x + 40) – 202.
e) 13(20 – 5x) = 15(30 – 5x) f) 14(7x – 14) + 3 = 12(8x + 20) + 1
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)
c) 8(3x – 5) = 60 + 20x d) 5x – 4(2 – 3x) = 22 + 7x3.
e) 3(x + 6) + 2(x + 1) = 40 f) 8(3x – 5) = 60 + 20x
a) 5x – 4(2 – 3x) = 22 + 7x b) 6(1 – 3x) + 7(4x – 3) = 35
c) 18q + 3 = 3(6,1q – 5) d) 5(x + 1,2) – 4 = 10x + 34.
e) 4(x + 9) – 34 = 2(x – 4) + 11 f) 8 – 10x – 2 = 8 – 5(x + 1,4)
Gleichungen – Klammer mal Klammer
a) (20 + x)(20 – x) = (x + 2)(46 – x) b) (x + 5)(5 – x) = (12 + x)(4 – x) + 1
c) (x – 5)(x + 8) = (x – 2)(x + 1) + 6 d) (x + 12)(x + 5) = (x – 8)(x + 7) – 101.
e) (x – 8)(x – 15) = (x – 8)(x – 25) f) (x + 9)(x – 17) = (x – 5)(x – 10)
a) (x +2)(x – 3) = x(x – 2) b) (2x + 4)(2x – 5) = (4x – 3)(x + 2)
c) (2x – 4)(3 – x) = (x + 4)(2 – 2x) d) x(3x + 2) = (3x – 6)(x + 2)2.
e) (x – 2)(x + 5) = (x + 6)(x – 1) f) (x – 2)(2x + 3) = (4 – x)(5 – 2x) + 1
a) (12 – x)(15 + x) = (8 – x)(9 + x) b) (15 – x)(20 + x) = (30 – x)(5 + x)
c) (x + 20)(x – 30) = (x – 10)(x + 40) d) (9 + x)(15 + x) = (3 + x)(5 + x)
e) (2x – 15)(3x + 4) = (6x – 4)(x + 12) – 117
3.
f) (x + 2)(3 – x) = (5 + x)(7 – x) + 2(x + 29)
Gleichungen mit Additions- und Subtraktionsklammern
a) 2x + (3x + 4) = 19 b) 12x + (3x + 4) + (2x + 3) = 41
c) 12x – 4 + (3x + 1) = 27 d) 8x – 3 + (x + 1) = 2x + 7 + (4x + 3)1.
e) 4 – (3x – 2) + 5x = 4 – (x + 1) f) (4x – 4) – 8 = –(3x – 2)
a) 12x + (13x – 19) – (11x – 15) = 25 – (17 – 13x)
b) (3x + 7) – 6 = 12x – (x + 4) – (4x – 5)
c) (5x – 3 ) – (2x – 4) = – (x + 3) – (x + 5) + (x + 3)
d) 12 – (5x + 8) – (8x – 12) = 14x – 25 – (3x – 8) + (7x + 2)
e) –(3x – 5) – (7x – 24) = 3 + (x + 1) – (2x – 7)
2.
f) 12x – (3x + 8) + (39 – 5x) = 14 + (25x – 8) – (41 – x)
a) 12x – 3 – (23x – 48) + (x + 93) = 58x – (24x – 44) + 6
b) –(19x + 51) – (11x + 4) = –(39x + 45) + (8x – 7) – 24
c) 24 – (14x – 8) – (3 + 12x) = 4 – (8x + 11)
d) 3,7 – (8,1x + 5,4) – (2,6x + 8,3) = –3,1x + (8 – 1,6x)
e) (4,5x + 56) – (2,25x – 7) – (300 – 3x) = – (0,75x – 3)
3.
f) 3,5x – 6 – (4 – 2x) = (2,4x – 9,4) – (1,2x – 25,2)
Gleichungen – Klammer mal Zahl
a) 7(x – 2) = 49 b) 7(5x + 2) + 9 = 58
c) 15(8x – 24) = 120 d) 6(3x – 25) = 121.
e) 12(5x – 2) = 48 + 12x f) 3(4x + 18) = 6x + 108
a) 23(2x + 5) = 6x + 315 b) 17(5x + 3) = 401 + 35x
c) 16(2x – 3) = 5(4x + 16) + 4 d) 12(8x – 25) = 5(16x + 40) – 202.
e) 13(20 – 5x) = 15(30 – 5x) f) 14(7x – 14) + 3 = 12(8x + 20) + 1
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)
c) 8(3x – 5) = 60 + 20x d) 5x – 4(2 – 3x) = 22 + 7x3.
e) 3(x + 6) + 2(x + 1) = 40 f) 8(3x – 5) = 60 + 20x
a) 5x – 4(2 – 3x) = 22 + 7x b) 6(1 – 3x) + 7(4x – 3) = 35
c) 18q + 3 = 3(6,1q – 5) d) 5(x + 1,2) – 4 = 10x + 34.
e) 4(x + 9) – 34 = 2(x – 4) + 11 f) 8 – 10x – 2 = 8 – 5(x + 1,4)
Gleichungen – Klammer mal Klammer
a) (20 + x)(20 – x) = (x + 2)(46 – x) b) (x + 5)(5 – x) = (12 + x)(4 – x) + 1
c) (x – 5)(x + 8) = (x – 2)(x + 1) + 6 d) (x + 12)(x + 5) = (x – 8)(x + 7) – 101.
e) (x – 8)(x – 15) = (x – 8)(x – 25) f) (x + 9)(x – 17) = (x – 5)(x – 10)
a) (x +2)(x – 3) = x(x – 2) b) (2x + 4)(2x – 5) = (4x – 3)(x + 2)
c) (2x – 4)(3 – x) = (x + 4)(2 – 2x) d) x(3x + 2) = (3x – 6)(x + 2)2.
e) (x – 2)(x + 5) = (x + 6)(x – 1) f) (x – 2)(2x + 3) = (4 – x)(5 – 2x) + 1
a) (12 – x)(15 + x) = (8 – x)(9 + x) b) (15 – x)(20 + x) = (30 – x)(5 + x)
c) (x + 20)(x – 30) = (x – 10)(x + 40) d) (9 + x)(15 + x) = (3 + x)(5 + x)
e) (2x – 15)(3x + 4) = (6x – 4)(x + 12) – 117
3.
f) (x + 2)(3 – x) = (5 + x)(7 – x) + 2(x + 29)
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Gleichungen mit 1 Variablen – verm. Übungen 1
a) 7x – (2x – 9) + (3x + 8) – (5x + 6) = 5 1. b) (4x – 5) – 6 = 12x – (x + 4) – (3x + 7)
a) 14x + (11x – 19) – (13x – 15) = 25 – (17 – 15x) 2. b) 26x – (14 + 19x) + (25 + 21x) = 29 – (–23x + 18)
a) 17 – (13 – 9x) + (16x – 9) = (15x – 22) – (7 – 4x) 3. b) 12 – (16 – 15x) + (11 – 9x) = (25 – 19x) – (13 – 23x)
a) 7x – [14 – (2x + 5)] = 18 – [3x + (15 – 4x)] 4. b) 4x – [7 – (x + 15)] = 11 – [5x – (3x – 17)]
a) 21x – [9 – (5x – 6) + 8x] = 15 – [(4x – 7) – (6x – 5)] 5. b) 19 – [13x – (22 + 7x) + 11] = 24x – [(15 – 4x) + (5x – 16)]
a) 12x – [14 – (9x – 11)] = 24x – [18 – (17x + 13)] 6. b) 17 – [13x – (15 – 19x) – 21x] = 25 – [(11x – 23) – (18x – 7)]
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)7. c) 8(4x – 3) = 4(5x – 6) d) 3(7x – 9) = 4(6x – 7)
a) 8 – 7(3x + 2) = 9x – 6(5x + 1) 8. b) 3x – 2(5x – 8) = 9 – 4(3x + 7)
a) 5(3x – 8) + 3(7x + 6) = 6(8x + 3) – 4(2x + 5) 9. b) 8(4x + 3) – 5(6x – 5) = 4(9x + 4) – 7(4x – 5)
a) 5(8x + 5) – 4(3x + 4) – 2(11x – 17) = 25 – 3(5x – 7) + 6(3x – 2)10. b) (2x – 3)7 – (x – 2)6 – (5x + 6)2 = 26 – (3x – 4)4 + (6x – 5)3
11. a) (x + 4)(3x – 7) = (x – 2)(3x + 8) b) (x + 5)(x + 2) = (x + 6)(x – 1)
12. a) (x – 4)(6 – x) = (x – 3)(8 – x) b) (x + 3)(2x + 5) = (x + 7)(2x – 1)
13. a) (x – 2)(x + 3) = (x + 4)(x – 5) b) (x + 1)(4x – 25) = (2x – 5)(2x – 8)
14. a) (x + 5)(x – 3) = (x + 6)(x – 2) b) (x – 7)(x – 4) = (x – 5)(x – 2)
15. a) (x – 4)(x – 3) = x² – 7x + 12 b) (2x – 5)(x + 1) = 2x² – 3x – 5
a) (5x – 6)(2x + 3) + (2x + 3)(3x – 2) = 2x(8x + 1) 16. b) (9x – 2)(2x – 5) + (3x + 4)(5x + 3) = 3x(11x – 3)
a) (3x – 4)(2x – 1) – (3x + 1)(x – 3) = (3x – 1)(x – 1) 17. b) (2x + 1)(3x – 1) – (2x + 11)(2x – 5) = (x – 6)(2x – 3)
a) (5x – 3)(2x – 3) – 2(4x – 1)(x – 3) = (2x – 3)(x + 5) 18. b) (3x + 1)(4x – 5) – 3(x – 3)(2x – 1) = (6x + 1)(x + 1)
a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)²
Gleichungen mit 1 Variablen – verm. Übungen 1
a) 7x – (2x – 9) + (3x + 8) – (5x + 6) = 5 1. b) (4x – 5) – 6 = 12x – (x + 4) – (3x + 7)
a) 14x + (11x – 19) – (13x – 15) = 25 – (17 – 15x) 2. b) 26x – (14 + 19x) + (25 + 21x) = 29 – (–23x + 18)
a) 17 – (13 – 9x) + (16x – 9) = (15x – 22) – (7 – 4x) 3. b) 12 – (16 – 15x) + (11 – 9x) = (25 – 19x) – (13 – 23x)
a) 7x – [14 – (2x + 5)] = 18 – [3x + (15 – 4x)] 4. b) 4x – [7 – (x + 15)] = 11 – [5x – (3x – 17)]
a) 21x – [9 – (5x – 6) + 8x] = 15 – [(4x – 7) – (6x – 5)] 5. b) 19 – [13x – (22 + 7x) + 11] = 24x – [(15 – 4x) + (5x – 16)]
a) 12x – [14 – (9x – 11)] = 24x – [18 – (17x + 13)] 6. b) 17 – [13x – (15 – 19x) – 21x] = 25 – [(11x – 23) – (18x – 7)]
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)7. c) 8(4x – 3) = 4(5x – 6) d) 3(7x – 9) = 4(6x – 7)
a) 8 – 7(3x + 2) = 9x – 6(5x + 1) 8. b) 3x – 2(5x – 8) = 9 – 4(3x + 7)
a) 5(3x – 8) + 3(7x + 6) = 6(8x + 3) – 4(2x + 5) 9. b) 8(4x + 3) – 5(6x – 5) = 4(9x + 4) – 7(4x – 5)
a) 5(8x + 5) – 4(3x + 4) – 2(11x – 17) = 25 – 3(5x – 7) + 6(3x – 2)10. b) (2x – 3)7 – (x – 2)6 – (5x + 6)2 = 26 – (3x – 4)4 + (6x – 5)3
11. a) (x + 4)(3x – 7) = (x – 2)(3x + 8) b) (x + 5)(x + 2) = (x + 6)(x – 1)
12. a) (x – 4)(6 – x) = (x – 3)(8 – x) b) (x + 3)(2x + 5) = (x + 7)(2x – 1)
13. a) (x – 2)(x + 3) = (x + 4)(x – 5) b) (x + 1)(4x – 25) = (2x – 5)(2x – 8)
14. a) (x + 5)(x – 3) = (x + 6)(x – 2) b) (x – 7)(x – 4) = (x – 5)(x – 2)
15. a) (x – 4)(x – 3) = x² – 7x + 12 b) (2x – 5)(x + 1) = 2x² – 3x – 5
a) (5x – 6)(2x + 3) + (2x + 3)(3x – 2) = 2x(8x + 1) 16. b) (9x – 2)(2x – 5) + (3x + 4)(5x + 3) = 3x(11x – 3)
a) (3x – 4)(2x – 1) – (3x + 1)(x – 3) = (3x – 1)(x – 1) 17. b) (2x + 1)(3x – 1) – (2x + 11)(2x – 5) = (x – 6)(2x – 3)
a) (5x – 3)(2x – 3) – 2(4x – 1)(x – 3) = (2x – 3)(x + 5) 18. b) (3x + 1)(4x – 5) – 3(x – 3)(2x – 1) = (6x + 1)(x + 1)
a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)²
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a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)² 19. b) (3x + 5)² + (2x – 3)² = (4x + 1)² – 3(x² – 1)
a) (x + 1)² – (x – 3)² = (x – 2)² – (x – 4)² 20. b) (4x + 3)² – (5x – 2)² = 6(x + 9) – (3x – 7)²
a) (x + 1)(x – 1) – (x – 3)² = (x + 4)² – (x – 2)(x + 2) 21. b) (x – 3)² – (x + 6)(x – 6) = (2x + 3)(2x – 3) – 4(x² – 15)
a) (2x + 1)² – (x – 4)² = (3x – 2)² – (2x + 1)(2x – 1) – 2(x² – 7x + 10) 22. b) (2x – 3)² + (3x + 5)² = (4x + 3)² – (3x – 2)(x + 6) – (2x – 7)
Gleichungen mit 1 Variablen – verm. Übungen 2
1. 5x + 4 – 6x + 8 = 3x + 4 – 8x – 7 + 3x
2. 18 – x – 15 + x + 2x = 18 – x + 19 + 3x – 1 – x
3. x – (x + 3) + x – 5 = 6 – (x – 4) + (x + 1)
4. 25x + 14 – (3x – 8) = 9x – (6x + 3) – 4x + (2 + 22x)
5. 5 – [x + 6 – (3 – x)] – 10x = 6x – [(3x + 2) – x] – 17x
6. 4(x – 3) + 5(x + 6) = 3 – 5(x + 3) + 13x
7. 5x – (6 – 3x) + 6(3x – 8) = 23x – 4(x – 5) + 6x
8. 172x + 19(24x – 17) = 207x – 18(61 – 18x) + 96x
9. 12(x + 13) – 14x + 5(x + 12) – 4(x + 3) = 0
10. 9x – {5x – [4x – (3x – 2) – 3] – 4} = 5x – 6 + x
11. x + 15 + 5(2x – 10) = 4x – (5 + x) + 2
12. 17(3x – 8) – [4x – (3 – x)] = 46x – 1 – 3(x + 2)
13. 31x – 58 + 4x – 16 = 5x + 24 + 9x – 18 + 4
14. 52(17x – 28) + 92(44 – 53x) = –51x + 20563 + 29(71x + 1)
15. 3x + 6(5x + 8) – 6 – (3 + x) – 6(x – 1) – 23x = 0
16. 2x + 3a – 5b + 4a – x = 4(a + b)
17. 12x – a – (a – x) = 14x + (a + b) – 3x + b
18. a + a² – b² – x = x – a + a² – b²
a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)² 19. b) (3x + 5)² + (2x – 3)² = (4x + 1)² – 3(x² – 1)
a) (x + 1)² – (x – 3)² = (x – 2)² – (x – 4)² 20. b) (4x + 3)² – (5x – 2)² = 6(x + 9) – (3x – 7)²
a) (x + 1)(x – 1) – (x – 3)² = (x + 4)² – (x – 2)(x + 2) 21. b) (x – 3)² – (x + 6)(x – 6) = (2x + 3)(2x – 3) – 4(x² – 15)
a) (2x + 1)² – (x – 4)² = (3x – 2)² – (2x + 1)(2x – 1) – 2(x² – 7x + 10) 22. b) (2x – 3)² + (3x + 5)² = (4x + 3)² – (3x – 2)(x + 6) – (2x – 7)
Gleichungen mit 1 Variablen – verm. Übungen 2
1. 5x + 4 – 6x + 8 = 3x + 4 – 8x – 7 + 3x
2. 18 – x – 15 + x + 2x = 18 – x + 19 + 3x – 1 – x
3. x – (x + 3) + x – 5 = 6 – (x – 4) + (x + 1)
4. 25x + 14 – (3x – 8) = 9x – (6x + 3) – 4x + (2 + 22x)
5. 5 – [x + 6 – (3 – x)] – 10x = 6x – [(3x + 2) – x] – 17x
6. 4(x – 3) + 5(x + 6) = 3 – 5(x + 3) + 13x
7. 5x – (6 – 3x) + 6(3x – 8) = 23x – 4(x – 5) + 6x
8. 172x + 19(24x – 17) = 207x – 18(61 – 18x) + 96x
9. 12(x + 13) – 14x + 5(x + 12) – 4(x + 3) = 0
10. 9x – {5x – [4x – (3x – 2) – 3] – 4} = 5x – 6 + x
11. x + 15 + 5(2x – 10) = 4x – (5 + x) + 2
12. 17(3x – 8) – [4x – (3 – x)] = 46x – 1 – 3(x + 2)
13. 31x – 58 + 4x – 16 = 5x + 24 + 9x – 18 + 4
14. 52(17x – 28) + 92(44 – 53x) = –51x + 20563 + 29(71x + 1)
15. 3x + 6(5x + 8) – 6 – (3 + x) – 6(x – 1) – 23x = 0
16. 2x + 3a – 5b + 4a – x = 4(a + b)
17. 12x – a – (a – x) = 14x + (a + b) – 3x + b
18. a + a² – b² – x = x – a + a² – b²
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19. ax + b + 2ax – 12b = 5ax – 3b – 6ax
20. (3a – x)² = (5a – x)²
21. (5 + x)²(a – b) = (5 + x)²(a + b) – 2bx²
Gleichungen mit 1 Variablen – verm. Übungen 3
Bestimme die Lösungsmenge zu folgenden Gleichungen.
a) 12x – 56 = 16 b) 5x + 39 = –26
4c) x 40 485 + = 3d) 1 x 4,2 7, 45 + =
e) 7x – 4 + 2x = 52 – 5x f) 40 – 2x + 5x = 68 + x
1.
g) 22x + 4(9 – 3x) = 46 h) 4(3x – 5) + 30 = 46
a) 18x – 75 + 3x + 128 – 7x = 68 – 8x – 25 + 14x
b) 113x + 73 – 5x – 16 = 23x + 85 – 33x + 45 + 62x + 151
c) 6x – 2(x – 16) = 5 – 3(11 – x) + 60
d) 4x – 5(x – 12) = 40 + 9(9 – x) – 11
3 2 e) (16x 24) 6(3x 4) (27x 18) 6x 34 3 + + − = + + −
2.
f) 3x – 15 + 2x = 18 + 4x + 25
a) 17x – 33 + 12x – 16 = 4x + 56 + 10x
b) –22x + 36 + 18x – 6 = 16x + 55 + 12x – 89
c) 4x – 22 + 3x – 45 = 8 – 2x + 26 + 5x – 1
d) 6x + 36 – 2x + 45 = 3x + 88 – 8x + 47
e) 12x – 66 – 34 + 2x = 8x – 35 + 2x + 99
3.
f) –12x + 25 + 6x – 38 = 66 + 2x – 22 + 3x – 12x
a) 66x + 14 – 39 + 12x – 100 = –12x – 47 + 23x + 56
b) 22x + 48 – 55x – 55x = 36 – 45 + 12x – 43
c) –22 + 14x – 33 + 10x – 77 + 25x = 88 – 14x + 65 – 5 + 35
d) –78 + 66x – 21x + 20 – 47 + 88x = 10x – 36 – 36x + 90
e) 55x – 44x – 12x –12x + 96 = 12x + 99 – 178 – 66x – 30
4.
f) –44 – 25x + 29 – 32x – 98x + 14x = –47x + 66 – 58x + 124 + 11
a) 12x – 33 + 20x – 78x + 36 – 48 + 30x – 45x + 558 – 14x – 605 – 58 = 0
b) –33x – 44x + 54 – 88 + 12x – 100 + 222x = 12 – 45x + 999 – 10x + 305 + 34
c) 36x – 78 + 61x – 69 – 78 + 22x – 47x = 369 – 44x + 45 – 12x + 78 + 120x + 11
d) –987x – 564 + 55x – 123 + 78 = –987x + 258 – 25x + 478 + 255
e) 16x² – 56x + 22 – 851 – 951 + 357x = 16x² + 698 – 14x + 548 – 20x – 11
5.
f) –65a + 58 – 36a + 587 – 33a = 698 + 14a – 587a + 698 – 32a +191
a) –789v + 258 – 11v + 456 – 894 = 336v + 201 – 45v + 710
b) 66z + 587 – 65z + 32z – 784 = –35z + 368 – 45z + 125 – 12
c) – 47y + 569 – 45y – 55y + 231 = –147y + 987 – 36y + 444 + 89
d) 665m – 478 – 365m + 884 – 320m = 6987 – 358 – 12m – 3365 + 6
e) –254a + 369 – 258 + 458a – 369 = –540a + 3320 + 142
6.
f) –258x + 5873 – 3369 + 368x – 897 – 321x + 33 = 1007
19. ax + b + 2ax – 12b = 5ax – 3b – 6ax
20. (3a – x)² = (5a – x)²
21. (5 + x)²(a – b) = (5 + x)²(a + b) – 2bx²
Gleichungen mit 1 Variablen – verm. Übungen 3
Bestimme die Lösungsmenge zu folgenden Gleichungen.
a) 12x – 56 = 16 b) 5x + 39 = –26
4c) x 40 485 + = 3d) 1 x 4,2 7, 45 + =
e) 7x – 4 + 2x = 52 – 5x f) 40 – 2x + 5x = 68 + x
1.
g) 22x + 4(9 – 3x) = 46 h) 4(3x – 5) + 30 = 46
a) 18x – 75 + 3x + 128 – 7x = 68 – 8x – 25 + 14x
b) 113x + 73 – 5x – 16 = 23x + 85 – 33x + 45 + 62x + 151
c) 6x – 2(x – 16) = 5 – 3(11 – x) + 60
d) 4x – 5(x – 12) = 40 + 9(9 – x) – 11
3 2 e) (16x 24) 6(3x 4) (27x 18) 6x 34 3 + + − = + + −
2.
f) 3x – 15 + 2x = 18 + 4x + 25
a) 17x – 33 + 12x – 16 = 4x + 56 + 10x
b) –22x + 36 + 18x – 6 = 16x + 55 + 12x – 89
c) 4x – 22 + 3x – 45 = 8 – 2x + 26 + 5x – 1
d) 6x + 36 – 2x + 45 = 3x + 88 – 8x + 47
e) 12x – 66 – 34 + 2x = 8x – 35 + 2x + 99
3.
f) –12x + 25 + 6x – 38 = 66 + 2x – 22 + 3x – 12x
a) 66x + 14 – 39 + 12x – 100 = –12x – 47 + 23x + 56
b) 22x + 48 – 55x – 55x = 36 – 45 + 12x – 43
c) –22 + 14x – 33 + 10x – 77 + 25x = 88 – 14x + 65 – 5 + 35
d) –78 + 66x – 21x + 20 – 47 + 88x = 10x – 36 – 36x + 90
e) 55x – 44x – 12x –12x + 96 = 12x + 99 – 178 – 66x – 30
4.
f) –44 – 25x + 29 – 32x – 98x + 14x = –47x + 66 – 58x + 124 + 11
a) 12x – 33 + 20x – 78x + 36 – 48 + 30x – 45x + 558 – 14x – 605 – 58 = 0
b) –33x – 44x + 54 – 88 + 12x – 100 + 222x = 12 – 45x + 999 – 10x + 305 + 34
c) 36x – 78 + 61x – 69 – 78 + 22x – 47x = 369 – 44x + 45 – 12x + 78 + 120x + 11
d) –987x – 564 + 55x – 123 + 78 = –987x + 258 – 25x + 478 + 255
e) 16x² – 56x + 22 – 851 – 951 + 357x = 16x² + 698 – 14x + 548 – 20x – 11
5.
f) –65a + 58 – 36a + 587 – 33a = 698 + 14a – 587a + 698 – 32a +191
a) –789v + 258 – 11v + 456 – 894 = 336v + 201 – 45v + 710
b) 66z + 587 – 65z + 32z – 784 = –35z + 368 – 45z + 125 – 12
c) – 47y + 569 – 45y – 55y + 231 = –147y + 987 – 36y + 444 + 89
d) 665m – 478 – 365m + 884 – 320m = 6987 – 358 – 12m – 3365 + 6
e) –254a + 369 – 258 + 458a – 369 = –540a + 3320 + 142
6.
f) –258x + 5873 – 3369 + 368x – 897 – 321x + 33 = 1007
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Einfache Gleichungen 1 – Lösungen
a) x + 3 = 8 b) x + 2 = 12 c) x + 9 = 18
L = { 5 } L = { 10 } L = { 9 }
d) x + 4 = 5 e) x + 22 = 44 f) x + 28 = 30
L = { 1 } L = { 22 } L = { 2 }
g) x + 7 = 2 h) x + 8 = –4 i) x + 2 = –12
1.
L = { –5 } L = { –12 } L = { –14 }
a) x – 1 = 2 b) x – 3 = 5 c) x – 4 = 11
L = { 3 } L = { 8 } L = { 15 }
d) x – 8 = 9 e) x – 2 = 13 f) x – 12 = 22
L = { 17 } L = { 15 } L = { 34 }
g) x – 7 = –11 h) x – 9 = –14 i) x – 1 = –19
2.
L = { –4 } L = { –5 } L = { –18 }
a) x 5 15 ⋅ = b) x 2 8 ⋅ = c) x 7 21 ⋅ =
L = { 3 } L = { 4 } L = { 3 }
d) 3 x 27 ⋅ = e) 9 x 45 ⋅ = f) 8 x 64 ⋅ =
L = { 9 } L = { 5 } L = { 8 }
g) x 2 4,2 ⋅ = h) 5 x 12,5 ⋅ = i) 9 x 1,8 ⋅ =
3.
L = { 2,1 } L = { 2,5 } L = { 0,2 }
xa) 22 = xb) 15 = xc) 98 =
L = { 4 } L = { 5 } L = { 72 }
xd) 95 = xe) 77 = xf ) 9 6 =
L = { 45 } L = { 49 } L = { 54 }
xg) 0,310 = xh) 1,14 = xi) 0,88 =
4.
L = { 3 } L = { 4,4 } L = { 6,4 }
a) x – 2 = 5 b) 3 + x = 1 xc) 412 = −
L = { 7 } L = { –2 } L = { –48 }
d) 3 x 3,6 ⋅ = e) x ( 4) 3,6 ⋅ − = − xf ) 1,1 3 = −
L = { 1,2 } L = { 0,9 } L = { –3,3 }
g) x + 1,8 = 2,2 h) x – 3,6 = 1,5 i) 3 x 1,5 − ⋅ = −
5.
L = { 0,4 } L = { 5,1 } L = { 0,5 }
a) 3 – x = 4 b) 2 – x = 8 c) 7 – x = 5
L = { –1 } L = { –6 } L = { 2 }
d) 9 – x = –3 e) 5 – x = – 8 f) –3 – x = –1
L = { 12 } L = { 13 } L = { –2 }
g) –2 – x = 6 h) 3 – x = 5 i) –4 – x = 12
6.
L = { –8 } L = { –2 } L = { –16 }
Einfache Gleichungen 1 – Lösungen
a) x + 3 = 8 b) x + 2 = 12 c) x + 9 = 18
L = { 5 } L = { 10 } L = { 9 }
d) x + 4 = 5 e) x + 22 = 44 f) x + 28 = 30
L = { 1 } L = { 22 } L = { 2 }
g) x + 7 = 2 h) x + 8 = –4 i) x + 2 = –12
1.
L = { –5 } L = { –12 } L = { –14 }
a) x – 1 = 2 b) x – 3 = 5 c) x – 4 = 11
L = { 3 } L = { 8 } L = { 15 }
d) x – 8 = 9 e) x – 2 = 13 f) x – 12 = 22
L = { 17 } L = { 15 } L = { 34 }
g) x – 7 = –11 h) x – 9 = –14 i) x – 1 = –19
2.
L = { –4 } L = { –5 } L = { –18 }
a) x 5 15 ⋅ = b) x 2 8 ⋅ = c) x 7 21 ⋅ =
L = { 3 } L = { 4 } L = { 3 }
d) 3 x 27 ⋅ = e) 9 x 45 ⋅ = f) 8 x 64 ⋅ =
L = { 9 } L = { 5 } L = { 8 }
g) x 2 4,2 ⋅ = h) 5 x 12,5 ⋅ = i) 9 x 1,8 ⋅ =
3.
L = { 2,1 } L = { 2,5 } L = { 0,2 }
xa) 22 = xb) 15 = xc) 98 =
L = { 4 } L = { 5 } L = { 72 }
xd) 95 = xe) 77 = xf ) 9 6 =
L = { 45 } L = { 49 } L = { 54 }
xg) 0,310 = xh) 1,14 = xi) 0,88 =
4.
L = { 3 } L = { 4,4 } L = { 6,4 }
a) x – 2 = 5 b) 3 + x = 1 xc) 412 = −
L = { 7 } L = { –2 } L = { –48 }
d) 3 x 3,6 ⋅ = e) x ( 4) 3,6 ⋅ − = − xf ) 1,1 3 = −
L = { 1,2 } L = { 0,9 } L = { –3,3 }
g) x + 1,8 = 2,2 h) x – 3,6 = 1,5 i) 3 x 1,5 − ⋅ = −
5.
L = { 0,4 } L = { 5,1 } L = { 0,5 }
a) 3 – x = 4 b) 2 – x = 8 c) 7 – x = 5
L = { –1 } L = { –6 } L = { 2 }
d) 9 – x = –3 e) 5 – x = – 8 f) –3 – x = –1
L = { 12 } L = { 13 } L = { –2 }
g) –2 – x = 6 h) 3 – x = 5 i) –4 – x = 12
6.
L = { –8 } L = { –2 } L = { –16 }
www.klassenarbeiten.de Seite 7
a) 3x + 4 = 16 b) 2x + 3 = 13 c) 4 + 5x = 19
L = { 4 } L = { 5 } L = { 3 }
d) 4x – 1 = 15 e) 9x – 8 = 19 f) 10x – 15 = 45
L = { 4 } L = { 3 } L = { 6 }
g) 5 – 2x = 15 h) 3 – 6x = 21 i) 9 – 5x = –36
7.
L = { –5 } L = { –3 } L = { 9 }
xa) 4 32 − = xb) 3 23+ = xc) 3 45 − =
L = { 14 } L = { –3 } L = { 35 }
xd) 8 25 + = xe) 4 58+ = 3xf ) 2 5 4 + =
L = { –30 } L = { 8 } L = { 4 }
2xg) 1 55 − = 5xh) 4 16− + = 2xi) 9 119+ =
8.
L = { 15 } L = { 6 } L = { 9 }
12a) 3x = 6b) 3x = 15c) 15x =
L = { 4 } L = { 2 } L = { 1 }
14d) 7x = 16e) 4x = 49f ) 7 x =
9.
L = { 2 } L = { 4 } L = { 7 }
Gleichungen mit Additions- und Subtraktionsklammern
Lösungen
a) 2x + (3x + 4) = 19 b) 12x + (3x + 4) + (2x + 3) = 41
L = { 3 } L = { 2 }
c) 12x – 4 + (3x + 1) = 27 d) 8x – 3 + (x + 1) = 2x + 7 + (4x + 3)
L = { 2 } L = { 4 }
e) 4 – (3x – 2) + 5x = 4 – (x + 1) f) (4x – 4) – 8 = – (3x – 2)
1.
L = { –1 } L = { 2 }
a) 12x + (13x – 19) – (11x – 15) = 25 – (17 – 13x)
L = { 12 }
b) (3x + 7) – 6 = 12x – (x + 4) – (4x – 5)
L = { 0 }
c) (5x – 3 ) – (2x – 4) = – (x + 3) – (x + 5) + (x + 3)
L = { –1,5 }
d) 12 – (5x + 8) – (8x – 12) = 14x – 25 – (3x – 8) + (7x + 2)
L = { 1 }
e) – (3x – 5) – (7x – 24) = 3 + (x + 1) – (2x – 7)
L = { 2 }
f) 12x – (3x + 8) + (39 – 5x) = 14 + (25x – 8) – (41 – x)
2.
L = { 3 }
a) 12x – 3 – (23x – 48) + (x + 93) = 58x – (24x – 44) + 6
L = { 2 }
b) – (19x + 51) – (11x + 4) = –(39x + 45) + (8x – 7) – 24
3.
L = { –21 }
a) 3x + 4 = 16 b) 2x + 3 = 13 c) 4 + 5x = 19
L = { 4 } L = { 5 } L = { 3 }
d) 4x – 1 = 15 e) 9x – 8 = 19 f) 10x – 15 = 45
L = { 4 } L = { 3 } L = { 6 }
g) 5 – 2x = 15 h) 3 – 6x = 21 i) 9 – 5x = –36
7.
L = { –5 } L = { –3 } L = { 9 }
xa) 4 32 − = xb) 3 23+ = xc) 3 45 − =
L = { 14 } L = { –3 } L = { 35 }
xd) 8 25 + = xe) 4 58+ = 3xf ) 2 5 4 + =
L = { –30 } L = { 8 } L = { 4 }
2xg) 1 55 − = 5xh) 4 16− + = 2xi) 9 119+ =
8.
L = { 15 } L = { 6 } L = { 9 }
12a) 3x = 6b) 3x = 15c) 15x =
L = { 4 } L = { 2 } L = { 1 }
14d) 7x = 16e) 4x = 49f ) 7 x =
9.
L = { 2 } L = { 4 } L = { 7 }
Gleichungen mit Additions- und Subtraktionsklammern
Lösungen
a) 2x + (3x + 4) = 19 b) 12x + (3x + 4) + (2x + 3) = 41
L = { 3 } L = { 2 }
c) 12x – 4 + (3x + 1) = 27 d) 8x – 3 + (x + 1) = 2x + 7 + (4x + 3)
L = { 2 } L = { 4 }
e) 4 – (3x – 2) + 5x = 4 – (x + 1) f) (4x – 4) – 8 = – (3x – 2)
1.
L = { –1 } L = { 2 }
a) 12x + (13x – 19) – (11x – 15) = 25 – (17 – 13x)
L = { 12 }
b) (3x + 7) – 6 = 12x – (x + 4) – (4x – 5)
L = { 0 }
c) (5x – 3 ) – (2x – 4) = – (x + 3) – (x + 5) + (x + 3)
L = { –1,5 }
d) 12 – (5x + 8) – (8x – 12) = 14x – 25 – (3x – 8) + (7x + 2)
L = { 1 }
e) – (3x – 5) – (7x – 24) = 3 + (x + 1) – (2x – 7)
L = { 2 }
f) 12x – (3x + 8) + (39 – 5x) = 14 + (25x – 8) – (41 – x)
2.
L = { 3 }
a) 12x – 3 – (23x – 48) + (x + 93) = 58x – (24x – 44) + 6
L = { 2 }
b) – (19x + 51) – (11x + 4) = –(39x + 45) + (8x – 7) – 24
3.
L = { –21 }
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c) 24 – (14x – 8) – (3 + 12x) = 4 – (8x + 11)
L = { 2 }
d) 3,7 – (8,1x + 5,4) – (2,6x + 8,3) = –3,1x + (8 – 1,6x)
L = { –3 }
e) (4,5x + 56) – (2,25x – 7) – (300 – 3x) = – (0,75x – 3)
L = { 40 }
f) 3,5x – 6 – (4 – 2x) = (2,4x – 9,4) – (1,2x – 25,2)
L = { 6 }
Gleichungen Klammer mal Zahl – Lösungen
a) 7(x – 2) = 49 b) 7(5x + 2) + 9 = 58
L = { 9 } L = { 1 }
c) 15(8x – 24) = 120 d) 6(3x – 25) = 12
L = { 4 } L = { 9 }
e) 12(5x – 2) = 48 + 12x f) 3(4x + 18) = 6x + 108
1.
L = { 1,5 } L = { 9 }
a) 23(2x + 5) = 6x + 315 b) 17(5x + 3) = 401 + 35x
L = { 5 } L = { 7 }
c) 16(2x – 3) = 5(4x + 16) + 4 d) 12(8x – 25) = 5(16x + 40) – 20
L = { 11 } L = { 30 }
e) 13(20 – 5x) = 15(30 – 5x) f) 14(7x – 14) + 3 = 12(8x + 20) + 1
2.
L = { 19 } L = { 217 }
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)
L = { –1 } L = G
c) 8(3x – 5) = 60 + 20x d) 5x – 4(2 – 3x) = 22 + 7x
L = { 25 } L = { 3 }
e) 3(x + 6) + 2(x + 1) = 40 f) 8(3x – 5) = 60 + 20x
3.
L = { 4 } L = { 25 }
a) 5x – 4(2 – 3x) = 22 + 7x b) 6(1 – 3x) + 7(4x – 3) = 35
L = { 3 } L = { 5 }
c) 18q + 3 = 3(6,1q – 5) d) 5(x + 1,2) – 4 = 10x + 3
L = { 60 } L = { –0,2 }
e) 4(x + 9) – 34 = 2(x – 4) + 11 f) 8 – 10x – 2 = 8 – 5(x + 1,4)
4.
L = { 0,5 } L = { 1 }
Gleichungen – Klammer mal Klammer – Lösungen
a) (20 + x)(20 – x) = (x + 2)(46 – x) b) (x + 5)(5 – x) = (12 + x)(4 – x) + 1
L = { 7 } L = { 3 }
c) (x – 5)(x + 8) = (x – 2)(x + 1) + 6 d) (x + 12)(x + 5) = (x – 8)(x + 7) – 10
L = { 11 } L = { –7 }
e) (x – 8)(x – 15) = (x – 8)(x – 25) f) (x + 9)(x – 17) = (x – 5)(x – 10)
1.
L = { 8 } L = { 29 }
a) (x +2)(x – 3) = x(x – 2) b) (2x + 4)(2x – 5) = (4x – 3)(x + 2)
L = { 6 } L = { –2 } 2.
c) (2x – 4)(3 – x) = (x + 4)(2 – 2x) d) x(3x + 2) = (3x – 6)(x + 2)
c) 24 – (14x – 8) – (3 + 12x) = 4 – (8x + 11)
L = { 2 }
d) 3,7 – (8,1x + 5,4) – (2,6x + 8,3) = –3,1x + (8 – 1,6x)
L = { –3 }
e) (4,5x + 56) – (2,25x – 7) – (300 – 3x) = – (0,75x – 3)
L = { 40 }
f) 3,5x – 6 – (4 – 2x) = (2,4x – 9,4) – (1,2x – 25,2)
L = { 6 }
Gleichungen Klammer mal Zahl – Lösungen
a) 7(x – 2) = 49 b) 7(5x + 2) + 9 = 58
L = { 9 } L = { 1 }
c) 15(8x – 24) = 120 d) 6(3x – 25) = 12
L = { 4 } L = { 9 }
e) 12(5x – 2) = 48 + 12x f) 3(4x + 18) = 6x + 108
1.
L = { 1,5 } L = { 9 }
a) 23(2x + 5) = 6x + 315 b) 17(5x + 3) = 401 + 35x
L = { 5 } L = { 7 }
c) 16(2x – 3) = 5(4x + 16) + 4 d) 12(8x – 25) = 5(16x + 40) – 20
L = { 11 } L = { 30 }
e) 13(20 – 5x) = 15(30 – 5x) f) 14(7x – 14) + 3 = 12(8x + 20) + 1
2.
L = { 19 } L = { 217 }
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)
L = { –1 } L = G
c) 8(3x – 5) = 60 + 20x d) 5x – 4(2 – 3x) = 22 + 7x
L = { 25 } L = { 3 }
e) 3(x + 6) + 2(x + 1) = 40 f) 8(3x – 5) = 60 + 20x
3.
L = { 4 } L = { 25 }
a) 5x – 4(2 – 3x) = 22 + 7x b) 6(1 – 3x) + 7(4x – 3) = 35
L = { 3 } L = { 5 }
c) 18q + 3 = 3(6,1q – 5) d) 5(x + 1,2) – 4 = 10x + 3
L = { 60 } L = { –0,2 }
e) 4(x + 9) – 34 = 2(x – 4) + 11 f) 8 – 10x – 2 = 8 – 5(x + 1,4)
4.
L = { 0,5 } L = { 1 }
Gleichungen – Klammer mal Klammer – Lösungen
a) (20 + x)(20 – x) = (x + 2)(46 – x) b) (x + 5)(5 – x) = (12 + x)(4 – x) + 1
L = { 7 } L = { 3 }
c) (x – 5)(x + 8) = (x – 2)(x + 1) + 6 d) (x + 12)(x + 5) = (x – 8)(x + 7) – 10
L = { 11 } L = { –7 }
e) (x – 8)(x – 15) = (x – 8)(x – 25) f) (x + 9)(x – 17) = (x – 5)(x – 10)
1.
L = { 8 } L = { 29 }
a) (x +2)(x – 3) = x(x – 2) b) (2x + 4)(2x – 5) = (4x – 3)(x + 2)
L = { 6 } L = { –2 } 2.
c) (2x – 4)(3 – x) = (x + 4)(2 – 2x) d) x(3x + 2) = (3x – 6)(x + 2)
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L = { 1,25 } L = { –6 }
e) (x – 2)(x + 5) = (x + 6)(x – 1) f) (x – 2)(2x + 3) = (4 – x)(5 – 2x) + 1
L = { –2 } L = { 2,25 }
a) (12 – x)(15 + x) = (8 – x)(9 + x) b) (15 – x)(20 + x) = (30 – x)(5 + x)
L = { 54 } L = { 5 }
c) (x + 20)(x – 30) = (x – 10)(x + 40) d) (9 + x)(15 + x) = (3 + x)(5 + x)
L = { –5 } L = { –7,5 }
e) (2x – 15)(3x + 4) = (6x – 4)(x + 12) – 117
L = { 1 }
f) (x + 2)(3 – x) = (5 + x)(7 – x) + 2(x + 29)
3.
L = { –29 }
Gleichungen mit 1 Variablen – verm. Übungen 1 –
Lösungen
a) 7x – (2x – 9) + (3x + 8) – (5x + 6) = 5
L = { –2 }
b) (4x – 5) – 6 = 12x – (x + 4) – (3x + 7)
1.
L = { 0 }
a) 14x + (11x – 19) – (13x – 15) = 25 – (17 – 15x)
L = { –4 }
b) 26x – (14 + 19x) + (25 + 21x) = 29 – (–23x + 18)
2.
L = { 0 }
a) 17 – (13 – 9x) + (16x – 9) = (15x – 22) – (7 – 4x)
L = { –4 }
b) 12 – (16 – 15x) + (11 – 9x) = (25 – 19x) – (13 – 23x)
3.
L = { 2,5 }
a) 7x – [14 – (2x + 5)] = 18 – [3x + (15 – 4x)]
L = { 1,5 }
b) 4x – [7 – (x + 15)] = 11 – [5x – (3x – 17)]
4.
L = { –2 }
a) 21x – [9 – (5x – 6) + 8x] = 15 – [(4x – 7) – (6x – 5)]
L = { 2 }
b) 19 – [13x – (22 + 7x) + 11] = 24x – [(15 – 4x) + (5x – 16)]
5.
L = { 1 }
a) 12x – [14 – (9x – 11)] = 24x – [18 – (17x + 13)]
L = { –1 }
b) 17 – [13x – (15 – 19x) – 21x] = 25 – [(11x – 23) – (18x – 7)]
6.
L = { –0,5 }
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)
L = { –1 } L = D
c) 8(4x – 3) = 4(5x – 6) d) 3(7x – 9) = 4(6x – 7)
7.
L = { 0 } 1L 3
⎧ ⎫= ⎨ ⎬⎩ ⎭
L = { 1,25 } L = { –6 }
e) (x – 2)(x + 5) = (x + 6)(x – 1) f) (x – 2)(2x + 3) = (4 – x)(5 – 2x) + 1
L = { –2 } L = { 2,25 }
a) (12 – x)(15 + x) = (8 – x)(9 + x) b) (15 – x)(20 + x) = (30 – x)(5 + x)
L = { 54 } L = { 5 }
c) (x + 20)(x – 30) = (x – 10)(x + 40) d) (9 + x)(15 + x) = (3 + x)(5 + x)
L = { –5 } L = { –7,5 }
e) (2x – 15)(3x + 4) = (6x – 4)(x + 12) – 117
L = { 1 }
f) (x + 2)(3 – x) = (5 + x)(7 – x) + 2(x + 29)
3.
L = { –29 }
Gleichungen mit 1 Variablen – verm. Übungen 1 –
Lösungen
a) 7x – (2x – 9) + (3x + 8) – (5x + 6) = 5
L = { –2 }
b) (4x – 5) – 6 = 12x – (x + 4) – (3x + 7)
1.
L = { 0 }
a) 14x + (11x – 19) – (13x – 15) = 25 – (17 – 15x)
L = { –4 }
b) 26x – (14 + 19x) + (25 + 21x) = 29 – (–23x + 18)
2.
L = { 0 }
a) 17 – (13 – 9x) + (16x – 9) = (15x – 22) – (7 – 4x)
L = { –4 }
b) 12 – (16 – 15x) + (11 – 9x) = (25 – 19x) – (13 – 23x)
3.
L = { 2,5 }
a) 7x – [14 – (2x + 5)] = 18 – [3x + (15 – 4x)]
L = { 1,5 }
b) 4x – [7 – (x + 15)] = 11 – [5x – (3x – 17)]
4.
L = { –2 }
a) 21x – [9 – (5x – 6) + 8x] = 15 – [(4x – 7) – (6x – 5)]
L = { 2 }
b) 19 – [13x – (22 + 7x) + 11] = 24x – [(15 – 4x) + (5x – 16)]
5.
L = { 1 }
a) 12x – [14 – (9x – 11)] = 24x – [18 – (17x + 13)]
L = { –1 }
b) 17 – [13x – (15 – 19x) – 21x] = 25 – [(11x – 23) – (18x – 7)]
6.
L = { –0,5 }
a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3)
L = { –1 } L = D
c) 8(4x – 3) = 4(5x – 6) d) 3(7x – 9) = 4(6x – 7)
7.
L = { 0 } 1L 3
⎧ ⎫= ⎨ ⎬⎩ ⎭
www.klassenarbeiten.de Seite 10
a) 8 – 7(3x + 2) = 9x – 6(5x + 1)
L = D
b) 3x – 2(5x – 8) = 9 – 4(3x + 7)
8.
L = { –7 }
a) 5(3x – 8) + 3(7x + 6) = 6(8x + 3) – 4(2x + 5)
L = { –5 }
b) 8(4x + 3) – 5(6x – 5) = 4(9x + 4) – 7(4x – 5)
9.
1L 3
⎧ ⎫ = − ⎨ ⎬ ⎩ ⎭
a) 5(8x + 5) – 4(3x + 4) – 2(11x – 17) = 25 – 3(5x – 7) + 6(3x – 2)
L = { –3 }
b) (2x – 3)7 – (x – 2)6 – (5x + 6)2 = 26 – (3x – 4)4 + (6x – 5)3
10.
L = { –6 }
a) (x + 4)(3x – 7) = (x – 2)(3x + 8) b) (x + 5)(x + 2) = (x + 6)(x – 1)11. L = { 4 } L = { –8 }
a) (x – 4)(6 – x) = (x – 3)(8 – x) b) (x + 3)(2x + 5) = (x + 7)(2x – 1)12. L = { 0 } L = { 11 }
a) (x – 2)(x + 3) = (x + 4)(x – 5) b) (x + 1)(4x – 25) = (2x – 5)(2x – 8)13. L = { –7 } L = { 13 }
a) (x + 5)(x – 3) = (x + 6)(x – 2) b) (x – 7)(x – 4) = (x – 5)(x – 2)14.
3L 2
⎧ ⎫ = − ⎨ ⎬ ⎩ ⎭
9L 2
⎧ ⎫= ⎨ ⎬⎩ ⎭
a) (x – 4)(x – 3) = x² – 7x + 12 b) (2x – 5)(x + 1) = 2x² – 3x – 515. L = D L = D
a) (5x – 6)(2x + 3) + (2x + 3)(3x – 2) = 2x(8x + 1)
L = { 4 }
b) (9x – 2)(2x – 5) + (3x + 4)(5x + 3) = 3x(11x – 3)
16.
L = { 2 }
a) (3x – 4)(2x – 1) – (3x + 1)(x – 3) = (3x – 1)(x – 1)
L = { –6 }
b) (2x + 1)(3x – 1) – (2x + 11)(2x – 5) = (x – 6)(2x – 3)
17.
L = { –9 }
a) (5x – 3)(2x – 3) – 2(4x – 1)(x – 3) = (2x – 3)(x + 5)
L = { 9 }
b) (3x + 1)(4x – 5) – 3(x – 3)(2x – 1) = (6x + 1)(x + 1)
18.
L = { 5 }
a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)²
L = { 5 }
b) (3x + 5)² + (2x – 3)² = (4x + 1)² – 3(x² – 1)
19.
L = { –3 }
a) 8 – 7(3x + 2) = 9x – 6(5x + 1)
L = D
b) 3x – 2(5x – 8) = 9 – 4(3x + 7)
8.
L = { –7 }
a) 5(3x – 8) + 3(7x + 6) = 6(8x + 3) – 4(2x + 5)
L = { –5 }
b) 8(4x + 3) – 5(6x – 5) = 4(9x + 4) – 7(4x – 5)
9.
1L 3
⎧ ⎫ = − ⎨ ⎬ ⎩ ⎭
a) 5(8x + 5) – 4(3x + 4) – 2(11x – 17) = 25 – 3(5x – 7) + 6(3x – 2)
L = { –3 }
b) (2x – 3)7 – (x – 2)6 – (5x + 6)2 = 26 – (3x – 4)4 + (6x – 5)3
10.
L = { –6 }
a) (x + 4)(3x – 7) = (x – 2)(3x + 8) b) (x + 5)(x + 2) = (x + 6)(x – 1)11. L = { 4 } L = { –8 }
a) (x – 4)(6 – x) = (x – 3)(8 – x) b) (x + 3)(2x + 5) = (x + 7)(2x – 1)12. L = { 0 } L = { 11 }
a) (x – 2)(x + 3) = (x + 4)(x – 5) b) (x + 1)(4x – 25) = (2x – 5)(2x – 8)13. L = { –7 } L = { 13 }
a) (x + 5)(x – 3) = (x + 6)(x – 2) b) (x – 7)(x – 4) = (x – 5)(x – 2)14.
3L 2
⎧ ⎫ = − ⎨ ⎬ ⎩ ⎭
9L 2
⎧ ⎫= ⎨ ⎬⎩ ⎭
a) (x – 4)(x – 3) = x² – 7x + 12 b) (2x – 5)(x + 1) = 2x² – 3x – 515. L = D L = D
a) (5x – 6)(2x + 3) + (2x + 3)(3x – 2) = 2x(8x + 1)
L = { 4 }
b) (9x – 2)(2x – 5) + (3x + 4)(5x + 3) = 3x(11x – 3)
16.
L = { 2 }
a) (3x – 4)(2x – 1) – (3x + 1)(x – 3) = (3x – 1)(x – 1)
L = { –6 }
b) (2x + 1)(3x – 1) – (2x + 11)(2x – 5) = (x – 6)(2x – 3)
17.
L = { –9 }
a) (5x – 3)(2x – 3) – 2(4x – 1)(x – 3) = (2x – 3)(x + 5)
L = { 9 }
b) (3x + 1)(4x – 5) – 3(x – 3)(2x – 1) = (6x + 1)(x + 1)
18.
L = { 5 }
a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)²
L = { 5 }
b) (3x + 5)² + (2x – 3)² = (4x + 1)² – 3(x² – 1)
19.
L = { –3 }
www.klassenarbeiten.de Seite 11
a) (x + 1)² – (x – 3)² = (x – 2)² – (x – 4)²
L = { –1 }
b) (4x + 3)² – (5x – 2)² = 6(x + 9) – (3x – 7)²
20.
L = { 0 }
a) (x + 1)(x – 1) – (x – 3)² = (x + 4)² – (x – 2)(x + 2)
L = { –15 }
b) (x – 3)² – (x + 6)(x – 6) = (2x + 3)(2x – 3) – 4(x² – 15)
21.
L = { –1 }
a) (2x + 1)² – (x – 4)² = (3x – 2)² – (2x + 1)(2x – 1) – 2(x² – 7x + 10)
L = { 0 }
b) (2x – 3)² + (3x + 5)² = (4x + 3)² – (3x – 2)(x + 6) – (2x – 7)
22.
L = { –0,5 }
Gleichungen mit 1 Variablen – verm. Übungen 2 –
Lösungen
1. 5x + 4 – 6x + 8 = 3x + 4 – 8x – 7 + 3x
L = { –15 }
2. 18 – x – 15 + x + 2x = 18 – x + 19 + 3x – 1 – x
L = { 33 }
3. x – (x + 3) + x – 5 = 6 – (x – 4) + (x + 1)
L = { 19 }
4. 25x + 14 – (3x – 8) = 9x – (6x + 3) – 4x + (2 + 22x)
L = { –23 }
5. 5 – [x + 6 – (3 – x)] – 10x = 6x – [(3x + 2) – x] – 17x
L = { –4 }
6. 4(x – 3) + 5(x + 6) = 3 – 5(x + 3) + 13x
L = { –30 }
7. 5x – (6 – 3x) + 6(3x – 8) = 23x – 4(x – 5) + 6x
L = { 74 }
8. 172x + 19(24x – 17) = 207x – 18(61 – 18x) + 96x
L = { –775 }
9. 12(x + 13) – 14x + 5(x + 12) – 4(x + 3) = 0
L = { 204 }
10. 9x – {5x – [4x – (3x – 2) – 3] – 4} = 5x – 6 + x
L = { 9 }
11. x + 15 + 5(2x – 10) = 4x – (5 + x) + 2
a) (x + 1)² – (x – 3)² = (x – 2)² – (x – 4)²
L = { –1 }
b) (4x + 3)² – (5x – 2)² = 6(x + 9) – (3x – 7)²
20.
L = { 0 }
a) (x + 1)(x – 1) – (x – 3)² = (x + 4)² – (x – 2)(x + 2)
L = { –15 }
b) (x – 3)² – (x + 6)(x – 6) = (2x + 3)(2x – 3) – 4(x² – 15)
21.
L = { –1 }
a) (2x + 1)² – (x – 4)² = (3x – 2)² – (2x + 1)(2x – 1) – 2(x² – 7x + 10)
L = { 0 }
b) (2x – 3)² + (3x + 5)² = (4x + 3)² – (3x – 2)(x + 6) – (2x – 7)
22.
L = { –0,5 }
Gleichungen mit 1 Variablen – verm. Übungen 2 –
Lösungen
1. 5x + 4 – 6x + 8 = 3x + 4 – 8x – 7 + 3x
L = { –15 }
2. 18 – x – 15 + x + 2x = 18 – x + 19 + 3x – 1 – x
L = { 33 }
3. x – (x + 3) + x – 5 = 6 – (x – 4) + (x + 1)
L = { 19 }
4. 25x + 14 – (3x – 8) = 9x – (6x + 3) – 4x + (2 + 22x)
L = { –23 }
5. 5 – [x + 6 – (3 – x)] – 10x = 6x – [(3x + 2) – x] – 17x
L = { –4 }
6. 4(x – 3) + 5(x + 6) = 3 – 5(x + 3) + 13x
L = { –30 }
7. 5x – (6 – 3x) + 6(3x – 8) = 23x – 4(x – 5) + 6x
L = { 74 }
8. 172x + 19(24x – 17) = 207x – 18(61 – 18x) + 96x
L = { –775 }
9. 12(x + 13) – 14x + 5(x + 12) – 4(x + 3) = 0
L = { 204 }
10. 9x – {5x – [4x – (3x – 2) – 3] – 4} = 5x – 6 + x
L = { 9 }
11. x + 15 + 5(2x – 10) = 4x – (5 + x) + 2
www.klassenarbeiten.de Seite 12
L = { 4 }
12. 17(3x – 8) – [4x – (3 – x)] = 46x – 1 – 3(x + 2)
L = { 42 }
13. 31x – 58 + 4x – 16 = 5x + 24 + 9x – 18 + 4
L = { 4 }
14. 52(17x – 28) + 92(44 – 53x) = –51x + 20563 + 29(71x + 1)
L = { –3 }
15. 3x + 6(5x + 8) – 6 – (3 + x) – 6(x – 1) – 23x = 0
L = { –15 }
16. 2x + 3a – 5b + 4a – x = 4(a + b)
L = { –3a + 9b }
17. 12x – a – (a – x) = 14x + (a + b) – 3x + b
L = { b + 1,5a }
18. a + a² – b² – x = x – a + a² – b²
L = { a }
19. ax + b + 2ax – 12b = 5ax – 3b – 6ax
2bL (mit a 0) a
⎧ ⎫ = ≠ ⎨ ⎬ ⎩ ⎭
20. (3a – x)² = (5a – x)²
L = { 4a } (mit a 0)≠
21. (5 + x)²(a – b) = (5 + x)²(a + b) – 2bx²
L = { –2,5 }
Gleichungen mit 1 Variablen – verm. Übungen 3 –
Lösungen
Bestimme die Lösungsmenge zu folgenden Gleichungen.
a) 12x – 56 = 16 b) 5x + 39 = –26
L = { 6 } L = { –13 }
4c) x 40 485 + = 3d) 1 x 4,2 7, 45 + =
L = { 10 } L = { 2 }
e) 7x – 4 + 2x = 52 – 5x f) 40 – 2x + 5x = 68 + x
L = { 4 } L = { 14 }
g) 22x + 4(9 – 3x) = 46 h) 4(3x – 5) + 30 = 46
1.
L = { 1 } L = { 3 }
L = { 4 }
12. 17(3x – 8) – [4x – (3 – x)] = 46x – 1 – 3(x + 2)
L = { 42 }
13. 31x – 58 + 4x – 16 = 5x + 24 + 9x – 18 + 4
L = { 4 }
14. 52(17x – 28) + 92(44 – 53x) = –51x + 20563 + 29(71x + 1)
L = { –3 }
15. 3x + 6(5x + 8) – 6 – (3 + x) – 6(x – 1) – 23x = 0
L = { –15 }
16. 2x + 3a – 5b + 4a – x = 4(a + b)
L = { –3a + 9b }
17. 12x – a – (a – x) = 14x + (a + b) – 3x + b
L = { b + 1,5a }
18. a + a² – b² – x = x – a + a² – b²
L = { a }
19. ax + b + 2ax – 12b = 5ax – 3b – 6ax
2bL (mit a 0) a
⎧ ⎫ = ≠ ⎨ ⎬ ⎩ ⎭
20. (3a – x)² = (5a – x)²
L = { 4a } (mit a 0)≠
21. (5 + x)²(a – b) = (5 + x)²(a + b) – 2bx²
L = { –2,5 }
Gleichungen mit 1 Variablen – verm. Übungen 3 –
Lösungen
Bestimme die Lösungsmenge zu folgenden Gleichungen.
a) 12x – 56 = 16 b) 5x + 39 = –26
L = { 6 } L = { –13 }
4c) x 40 485 + = 3d) 1 x 4,2 7, 45 + =
L = { 10 } L = { 2 }
e) 7x – 4 + 2x = 52 – 5x f) 40 – 2x + 5x = 68 + x
L = { 4 } L = { 14 }
g) 22x + 4(9 – 3x) = 46 h) 4(3x – 5) + 30 = 46
1.
L = { 1 } L = { 3 }
www.klassenarbeiten.de Seite 13
a) 18x – 75 + 3x + 128 – 7x = 68 – 8x – 25 + 14x
L = { –1,25 }
b) 113x + 73 – 5x – 16 = 23x + 85 – 33x + 45 + 62x + 151
L = { 4 }
c) 6x – 2(x – 16) = 5 – 3(11 – x) + 60
L = { 0 }
d) 4x – 5(x – 12) = 40 + 9(9 – x) – 11
L = { 6,25 }
3 2 e) (16x 24) 6(3x 4) (27x 18) 6x 34 3 + + − = + + −
L = { 2,5 }
f) 3x – 15 + 2x = 18 + 4x + 25
2.
L = { 58 }
a) 17x – 33 + 12x – 16 = 4x + 56 + 10x
L = { 7 }
b) –22x + 36 + 18x – 6 = 16x + 55 + 12x – 89
L = { 2 }
c) 4x – 22 + 3x – 45 = 8 – 2x + 26 + 5x – 1
L = { 25 }
d) 6x + 36 – 2x + 45 = 3x + 88 – 8x + 47
L = { 6 }
e) 12x – 66 – 34 + 2x = 8x – 35 + 2x + 99
L = { 41 }
f) –12x + 25 + 6x – 38 = 66 + 2x – 22 + 3x – 12x
3.
L = { 57 }
a) 66x + 14 – 39 + 12x – 100 = –12x – 47 + 23x + 56
L = { 2 }
b) 22x + 48 – 55x – 55x = 36 – 45 + 12x – 43
L = { 1 }
c) –22 + 14x – 33 + 10x – 77 + 25x = 88 – 14x + 65 – 5 + 35
L = { 5 }
d) –78 + 66x – 21x + 20 – 47 + 88x = 10x – 36 – 36x + 90
L = { 1 }
e) 55x – 44x – 12x –12x + 96 = 12x + 99 – 178 – 66x – 30
L = { –5 }
f) –44 – 25x + 29 – 32x – 98x + 14x = –47x + 66 – 58x + 124 + 11
4.
L = { –6 }
a) 12x – 33 + 20x – 78x + 36 – 48 + 30x – 45x + 558 – 14x – 605 – 58 = 0
L = { –2 }
b) –33x – 44x + 54 – 88 + 12x – 100 + 222x = 12 – 45x + 999 – 10x + 305 + 34
L = { 7 }
c) 36x – 78 + 61x – 69 – 78 + 22x – 47x = 369 – 44x + 45 – 12x + 78 + 120x + 11
L = { 91 }
d) –987x – 564 + 55x – 123 + 78 = –987x + 258 – 25x + 478 + 255
L = { 20 }
e) 16x² – 56x + 22 – 851 – 951 + 357x = 16x² + 698 – 14x + 548 – 20x – 11
L = { 9 }
f) –65a + 58 – 36a + 587 – 33a = 698 + 14a – 587a + 698 – 32a + 191
5.
L = { 2 }
a) 18x – 75 + 3x + 128 – 7x = 68 – 8x – 25 + 14x
L = { –1,25 }
b) 113x + 73 – 5x – 16 = 23x + 85 – 33x + 45 + 62x + 151
L = { 4 }
c) 6x – 2(x – 16) = 5 – 3(11 – x) + 60
L = { 0 }
d) 4x – 5(x – 12) = 40 + 9(9 – x) – 11
L = { 6,25 }
3 2 e) (16x 24) 6(3x 4) (27x 18) 6x 34 3 + + − = + + −
L = { 2,5 }
f) 3x – 15 + 2x = 18 + 4x + 25
2.
L = { 58 }
a) 17x – 33 + 12x – 16 = 4x + 56 + 10x
L = { 7 }
b) –22x + 36 + 18x – 6 = 16x + 55 + 12x – 89
L = { 2 }
c) 4x – 22 + 3x – 45 = 8 – 2x + 26 + 5x – 1
L = { 25 }
d) 6x + 36 – 2x + 45 = 3x + 88 – 8x + 47
L = { 6 }
e) 12x – 66 – 34 + 2x = 8x – 35 + 2x + 99
L = { 41 }
f) –12x + 25 + 6x – 38 = 66 + 2x – 22 + 3x – 12x
3.
L = { 57 }
a) 66x + 14 – 39 + 12x – 100 = –12x – 47 + 23x + 56
L = { 2 }
b) 22x + 48 – 55x – 55x = 36 – 45 + 12x – 43
L = { 1 }
c) –22 + 14x – 33 + 10x – 77 + 25x = 88 – 14x + 65 – 5 + 35
L = { 5 }
d) –78 + 66x – 21x + 20 – 47 + 88x = 10x – 36 – 36x + 90
L = { 1 }
e) 55x – 44x – 12x –12x + 96 = 12x + 99 – 178 – 66x – 30
L = { –5 }
f) –44 – 25x + 29 – 32x – 98x + 14x = –47x + 66 – 58x + 124 + 11
4.
L = { –6 }
a) 12x – 33 + 20x – 78x + 36 – 48 + 30x – 45x + 558 – 14x – 605 – 58 = 0
L = { –2 }
b) –33x – 44x + 54 – 88 + 12x – 100 + 222x = 12 – 45x + 999 – 10x + 305 + 34
L = { 7 }
c) 36x – 78 + 61x – 69 – 78 + 22x – 47x = 369 – 44x + 45 – 12x + 78 + 120x + 11
L = { 91 }
d) –987x – 564 + 55x – 123 + 78 = –987x + 258 – 25x + 478 + 255
L = { 20 }
e) 16x² – 56x + 22 – 851 – 951 + 357x = 16x² + 698 – 14x + 548 – 20x – 11
L = { 9 }
f) –65a + 58 – 36a + 587 – 33a = 698 + 14a – 587a + 698 – 32a + 191
5.
L = { 2 }
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a) –789v + 258 – 11v + 456 – 894 = 336v + 201 – 45v + 710
L = { –1 }
b) 66z + 587 – 65z + 32z – 784 = –35z + 368 – 45z + 125 – 12
L = { 6 }
c) – 47y + 569 – 45y – 55y + 231 = –147y + 987 – 36y + 444 + 89
L = { 20 }
d) 665m – 478 – 365m + 884 – 320m = 6987 – 358 – 12m – 3365 + 6
L = { –358 }
e) –254a + 369 – 258 + 458a – 369 = –540a + 3320 + 142
L = { 5 }
f) –258x + 5873 – 3369 + 368x – 897 – 321x + 33 = 1007
6.
L = { 3 }
a) –789v + 258 – 11v + 456 – 894 = 336v + 201 – 45v + 710
L = { –1 }
b) 66z + 587 – 65z + 32z – 784 = –35z + 368 – 45z + 125 – 12
L = { 6 }
c) – 47y + 569 – 45y – 55y + 231 = –147y + 987 – 36y + 444 + 89
L = { 20 }
d) 665m – 478 – 365m + 884 – 320m = 6987 – 358 – 12m – 3365 + 6
L = { –358 }
e) –254a + 369 – 258 + 458a – 369 = –540a + 3320 + 142
L = { 5 }
f) –258x + 5873 – 3369 + 368x – 897 – 321x + 33 = 1007
6.
L = { 3 }
