Simplifying and Solving Equations worksheet with algebra problems for practice.

Sure! Let’s solve each of the 20 equations step by step. The goal is to simplify and solve for the unknown variable in each equation.

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Equation 1:

2(3 - A) = 6 - 5A

- Distribute left side:
→ 6 - 2A = 6 - 5A

- Subtract 6 from both sides:
→ -2A = -5A

- Add 5A to both sides:
→ 3A = 0

- Divide by 3:
→ A = 0

✔ Answer: A = 0

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Equation 2:

2(3b - 2) + 9 = -5b

- Distribute:
→ 6b - 4 + 9 = -5b
→ 6b + 5 = -5b

- Add 5b to both sides:
→ 11b + 5 = 0

- Subtract 5:
→ 11b = -5

- Divide by 11:
→ b = -5/11

✔ Answer: b = -5/11

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Equation 3:

7 + 9d - 7d = 3

- Combine like terms:
→ 7 + 2d = 3

- Subtract 7:
→ 2d = -4

- Divide by 2:
→ d = -2

✔ Answer: d = -2

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Equation 4:

3(3 - p) = -5(p + 1)

- Distribute both sides:
→ 9 - 3p = -5p - 5

- Add 5p to both sides:
→ 9 + 2p = -5

- Subtract 9:
→ 2p = -14

- Divide by 2:
→ p = -7

✔ Answer: p = -7

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Equation 5:

-2(4 + 3q) = -2(4 + q)

- Distribute both sides:
→ -8 - 6q = -8 - 2q

- Add 8 to both sides:
→ -6q = -2q

- Add 6q to both sides:
→ 0 = 4q

- → q = 0

✔ Answer: q = 0

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Equation 6:

3(3 - 3g) = -7 + g

- Distribute left:
→ 9 - 9g = -7 + g

- Add 9g to both sides:
→ 9 = -7 + 10g

- Add 7:
→ 16 = 10g

- Divide by 10:
→ g = 16/10 = 8/5

✔ Answer: g = 8/5

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Equation 7:

-7 + 4c = 7(c + 4)

- Distribute right:
→ -7 + 4c = 7c + 28

- Subtract 4c:
→ -7 = 3c + 28

- Subtract 28:
→ -35 = 3c

- Divide by 3:
→ c = -35/3

✔ Answer: c = -35/3

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Equation 8:

1 + 18 = -8 + 9

Wait — this has no variable! Let’s check:

Left: 1 + 18 = 19
Right: -8 + 9 = 1
→ 19 = 1? ✘ False statement

But the instruction says “Determine the value of the unknown in each equation.” Since there’s no variable, this might be a trick or typo.

If we assume it's meant to be an identity or solve for nothing, then no solution (contradiction).

But perhaps it was meant to have a variable? Let’s assume it’s miswritten.

Alternatively, if it’s just evaluating, it’s false.

But since the worksheet expects a variable solution, I’ll note:

⚠️ No variable — likely error. If forced to answer: no solution.

But let’s double-check — maybe it’s 1 + 18h = -8 + 9h? Not written that way.

I’ll mark it as invalid / no variable.

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Actually, looking again — maybe it’s Equation 8: 1 + 18 = -8 + 9 — but that’s not an equation with a variable. Probably a mistake.

Let’s skip and come back if needed.

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Equation 9:

5(1 + t) = -9t + 6

- Distribute:
→ 5 + 5t = -9t + 6

- Add 9t:
→ 5 + 14t = 6

- Subtract 5:
→ 14t = 1

- Divide:
→ t = 1/14

✔ Answer: t = 1/14

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Equation 10:

2z + 8 = 5z - 1

- Subtract 2z:
→ 8 = 3z - 1

- Add 1:
→ 9 = 3z

- Divide:
→ z = 3

✔ Answer: z = 3

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Equation 11:

3 + x = 2(2x - 1)

- Distribute right:
→ 3 + x = 4x - 2

- Subtract x:
→ 3 = 3x - 2

- Add 2:
→ 5 = 3x

- Divide:
→ x = 5/3

✔ Answer: x = 5/3

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Equation 12:

5a - 2 = -8a + 8

- Add 8a:
→ 13a - 2 = 8

- Add 2:
→ 13a = 10

- Divide:
→ a = 10/13

✔ Answer: a = 10/13

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Equation 13:

-2 - 4w = 7w - 8

- Add 4w:
→ -2 = 11w - 8

- Add 8:
→ 6 = 11w

- Divide:
→ w = 6/11

✔ Answer: w = 6/11

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Equation 14:

6d - 6 = -9d - 9

- Add 9d:
→ 15d - 6 = -9

- Add 6:
→ 15d = -3

- Divide:
→ d = -3/15 = -1/5

✔ Answer: d = -1/5

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Equation 15:

-6(3 - m) = 9 - 2m

- Distribute left:
→ -18 + 6m = 9 - 2m

- Add 2m:
→ -18 + 8m = 9

- Add 18:
→ 8m = 27

- Divide:
→ m = 27/8

✔ Answer: m = 27/8

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Equation 16:

-1 + 3f = -7 - 4f

- Add 4f:
→ -1 + 7f = -7

- Add 1:
→ 7f = -6

- Divide:
→ f = -6/7

✔ Answer: f = -6/7

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Equation 17:

-2q - 3 = -2(2q + 1)

- Distribute right:
→ -2q - 3 = -4q - 2

- Add 4q:
→ 2q - 3 = -2

- Add 3:
→ 2q = 1

- Divide:
→ q = 1/2

✔ Answer: q = 1/2

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Equation 18:

2 + r = 7 - 4r

- Add 4r:
→ 2 + 5r = 7

- Subtract 2:
→ 5r = 5

- Divide:
→ r = 1

✔ Answer: r = 1

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Equation 19:

6x + 7 = 3x + 5

- Subtract 3x:
→ 3x + 7 = 5

- Subtract 7:
→ 3x = -2

- Divide:
→ x = -2/3

✔ Answer: x = -2/3

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Equation 20:

-6k + 1 = -2 + 7k

- Add 6k:
→ 1 = -2 + 13k

- Add 2:
→ 3 = 13k

- Divide:
→ k = 3/13

✔ Answer: k = 3/13

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## 📝 Final Answers Summary:

1. A = 0
2. b = -5/11
3. d = -2
4. p = -7
5. q = 0
6. g = 8/5
7. c = -35/3
8. No variable — invalid / contradiction *(see note below)*
9. t = 1/14
10. z = 3
11. x = 5/3
12. a = 10/13
13. w = 6/11
14. d = -1/5
15. m = 27/8
16. f = -6/7
17. q = 1/2
18. r = 1
19. x = -2/3
20. k = 3/13

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## ⚠️ Note on Equation 8:
> 8. 1 + 18 = -8 + 9

This simplifies to 19 = 1, which is false. Since there’s no variable, it’s not solvable for an unknown. It may be a typo — perhaps meant to be 1 + 18h = -8 + 9h or similar. As written, no solution (or undefined).

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✔ All other equations solved correctly with steps shown.

Let me know if you’d like them boxed or formatted differently!