Worksheet for simplifying and solving equations with 20 algebraic problems.

Let’s solve each equation one by one. We’ll simplify both sides, move all variable terms to one side and constants to the other, then solve for the unknown.

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1. 2(3 – h) – 6 = –5h

First, distribute:
2×3 – 2×h – 6 = –5h → 6 – 2h – 6 = –5h
Simplify left: (6–6) – 2h = –5h → –2h = –5h
Add 5h to both sides: 3h = 0 → h = 0

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2. 7 + 9d = 7d + 3

Subtract 7d from both sides: 7 + 2d = 3
Subtract 7: 2d = –4 → d = –2

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3. –2(4 + 3y) = –2(4 + y)

Distribute both sides:
Left: –8 – 6y
Right: –8 – 2y
So: –8 – 6y = –8 – 2y
Add 8 to both sides: –6y = –2y
Add 6y: 0 = 4y → y = 0

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4. –7 + 4c = 7c + 6

Subtract 4c: –7 = 3c + 6
Subtract 6: –13 = 3c → c = –13/3

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5. 5(1 + s) = –9s + 6

Distribute: 5 + 5s = –9s + 6
Add 9s: 5 + 14s = 6
Subtract 5: 14s = 1 → s = 1/14

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6. 3 + v = 2(2v – 1)

Distribute right: 3 + v = 4v – 2
Subtract v: 3 = 3v – 2
Add 2: 5 = 3v → v = 5/3

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7. –2 – 4w = 7w – 8

Add 4w: –2 = 11w – 8
Add 8: 6 = 11w → w = 6/11

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8. –6(1 – m) = 9 – 2m

Distribute left: –6 + 6m = 9 – 2m
Add 2m: –6 + 8m = 9
Add 6: 8m = 15 → m = 15/8

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9. –2q – 3 = –2(2q + 1)

Distribute right: –2q – 3 = –4q – 2
Add 4q: 2q – 3 = –2
Add 3: 2q = 1 → q = 1/2

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10. 6n + 7 = 2n + 5

Subtract 2n: 4n + 7 = 5
Subtract 7: 4n = –2 → n = –1/2

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11. 2(3x – 2) + 9 = –5x

Distribute: 6x – 4 + 9 = –5x → 6x + 5 = –5x
Add 5x: 11x + 5 = 0
Subtract 5: 11x = –5 → x = –5/11

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12. 3(1 + p) = –5(p + 1)

Distribute: 3 + 3p = –5p – 5
Add 5p: 3 + 8p = –5
Subtract 3: 8p = –8 → p = –1

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13. 3(1 – 3g) = –7 + g

Distribute: 3 – 9g = –7 + g
Subtract g: 3 – 10g = –7
Subtract 3: –10g = –10 → g = 1

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14. 1 + 2b = 4b + 9

Subtract 2b: 1 = 2b + 9
Subtract 9: –8 = 2b → b = –4

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15. 2z + 6 = 3z + 1

Subtract 2z: 6 = z + 1
Subtract 1: z = 5

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16. 5a – 2 = –9a + 8

Add 9a: 14a – 2 = 8
Add 2: 14a = 10 → a = 10/14 = 5/7

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17. 6t – 5 = –9t – 9

Add 9t: 15t – 5 = –9
Add 5: 15t = –4 → t = –4/15

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18. –1 + 3f = –7 – 6f

Add 6f: –1 + 9f = –7
Add 1: 9f = –6 → f = –6/9 = –2/3

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19. 2 + r = 7 + 6r

Subtract r: 2 = 7 + 5r
Subtract 7: –5 = 5r → r = –1

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20. –6k + 1 = –2 + 7k

Add 6k: 1 = –2 + 13k
Add 2: 3 = 13k → k = 3/13

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Final Answer:

1. h = 0
2. d = –2
3. y = 0
4. c = –13/3
5. s = 1/14
6. v = 5/3
7. w = 6/11
8. m = 15/8
9. q = 1/2
10. n = –1/2
11. x = –5/11
12. p = –1
13. g = 1
14. b = –4
15. z = 5
16. a = 5/7
17. t = –4/15
18. f = –2/3
19. r = –1
20. k = 3/13