Grade 8 Math Worksheet: Solve for x in each of the following equations.

Of course! I'll solve each of the 10 equations for `x` step by step and explain the process clearly. These are all linear equations, so we’ll use inverse operations to isolate `x`.

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1. 2x + 5 = 17

Goal: Get `x` alone on one side.

- Subtract 5 from both sides:
> 2x = 17 - 5
> 2x = 12

- Divide both sides by 2:
> x = 12 ÷ 2
> x = 6

✔ Answer: x = 6

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2. 3(x - 4) = 15

Goal: Distribute first, then isolate `x`.

- Distribute the 3:
> 3x - 12 = 15

- Add 12 to both sides:
> 3x = 15 + 12
> 3x = 27

- Divide by 3:
> x = 27 ÷ 3
> x = 9

✔ Answer: x = 9

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3. 4x - 7 = 3x + 11

Goal: Get all `x` terms on one side, constants on the other.

- Subtract 3x from both sides:
> 4x - 3x - 7 = 11
> x - 7 = 11

- Add 7 to both sides:
> x = 11 + 7
> x = 18

✔ Answer: x = 18

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4. 5(2x + 1) = 25 - x

Goal: Distribute, then collect like terms.

- Distribute the 5:
> 10x + 5 = 25 - x

- Add x to both sides (to move all x’s left):
> 10x + x + 5 = 25
> 11x + 5 = 25

- Subtract 5 from both sides:
> 11x = 20

- Divide by 11:
> x = 20/11

✔ Answer: x = 20/11 (or approximately 1.818...)

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5. 3x - 4 = 5 - 2x

Goal: Move variables to one side, constants to the other.

- Add 2x to both sides:
> 3x + 2x - 4 = 5
> 5x - 4 = 5

- Add 4 to both sides:
> 5x = 9

- Divide by 5:
> x = 9/5

✔ Answer: x = 9/5 (or 1.8)

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6. 2(3x - 1) + 5x = 13

Goal: Distribute, combine like terms, then solve.

- Distribute the 2:
> 6x - 2 + 5x = 13

- Combine like terms:
> 11x - 2 = 13

- Add 2 to both sides:
> 11x = 15

- Divide by 11:
> x = 15/11

✔ Answer: x = 15/11 (approximately 1.364...)

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7. 2(x + 3) - 5(x - 2) = 3

Goal: Distribute carefully, combine like terms.

- Distribute:
> 2x + 6 - 5x + 10 = 3
*(Note: -5 times -2 is +10)*

- Combine like terms:
> (2x - 5x) + (6 + 10) = 3
> -3x + 16 = 3

- Subtract 16 from both sides:
> -3x = 3 - 16
> -3x = -13

- Divide by -3:
> x = 13/3

✔ Answer: x = 13/3 (or 4 1/3)

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8. 3(x - 1) + 2(2x + 1) = 11

Goal: Distribute, combine, solve.

- Distribute:
> 3x - 3 + 4x + 2 = 11
*(2 × 2x = 4x; 2 × 1 = 2)*

- Combine like terms:
> (3x + 4x) + (-3 + 2) = 11
> 7x - 1 = 11

- Add 1 to both sides:
> 7x = 12

- Divide by 7:
> x = 12/7

✔ Answer: x = 12/7 (approximately 1.714...)

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9. 2x - 1 = x + 5

Goal: Move x terms to one side.

- Subtract x from both sides:
> 2x - x - 1 = 5
> x - 1 = 5

- Add 1 to both sides:
> x = 6

✔ Answer: x = 6

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10. 5(x + 3) - 3(x - 1) = 22

Goal: Distribute, combine, solve.

- Distribute:
> 5x + 15 - 3x + 3 = 22
*(Note: -3 times -1 is +3)*

- Combine like terms:
> (5x - 3x) + (15 + 3) = 22
> 2x + 18 = 22

- Subtract 18 from both sides:
> 2x = 4

- Divide by 2:
> x = 2

✔ Answer: x = 2

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## ✔ Final Answers Summary:

1. x = 6
2. x = 9
3. x = 18
4. x = 20/11
5. x = 9/5
6. x = 15/11
7. x = 13/3
8. x = 12/7
9. x = 6
10. x = 2

Let me know if you’d like to see any of these explained in more detail or want to check your own work!