GRADE 8 +9 MATH WORKSHEETS - Like terms and solving linear ... - Free Printable

Let's solve each equation step by step. We are solving for $ x $ in each of the following equations.

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1. $ 2x + 5 = 17 $

Step 1: Subtract 5 from both sides:
$ 2x = 17 - 5 $
$ 2x = 12 $

Step 2: Divide both sides by 2:
$ x = \frac{12}{2} = 6 $

✔ Answer: $ x = 6 $

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2. $ 3(x - 4) = 15 $

Step 1: Distribute the 3:
$ 3x - 12 = 15 $

Step 2: Add 12 to both sides:
$ 3x = 15 + 12 = 27 $

Step 3: Divide by 3:
$ x = \frac{27}{3} = 9 $

✔ Answer: $ x = 9 $

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3. $ 4x - 7 = 3x + 11 $

Step 1: Subtract $ 3x $ from both sides:
$ 4x - 3x - 7 = 11 $
$ x - 7 = 11 $

Step 2: Add 7 to both sides:
$ x = 11 + 7 = 18 $

✔ Answer: $ x = 18 $

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

Step 1: Distribute the 5:
$ 10x + 5 = 25 - x $

Step 2: Add $ x $ to both sides:
$ 10x + x + 5 = 25 $
$ 11x + 5 = 25 $

Step 3: Subtract 5 from both sides:
$ 11x = 20 $

Step 4: Divide by 11:
$ x = \frac{20}{11} $

✔ Answer: $ x = \frac{20}{11} $ (or approximately $ 1.818 $)

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5. $ 3x - 4 = 5 - 2x $

Step 1: Add $ 2x $ to both sides:
$ 3x + 2x - 4 = 5 $
$ 5x - 4 = 5 $

Step 2: Add 4 to both sides:
$ 5x = 9 $

Step 3: Divide by 5:
$ x = \frac{9}{5} = 1.8 $

✔ Answer: $ x = \frac{9}{5} $

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

Step 1: Distribute the 2:
$ 6x - 2 + 5x = 13 $

Step 2: Combine like terms:
$ 11x - 2 = 13 $

Step 3: Add 2 to both sides:
$ 11x = 15 $

Step 4: Divide by 11:
$ x = \frac{15}{11} $

✔ Answer: $ x = \frac{15}{11} $ (≈ 1.364)

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

Step 1: Distribute:
$ 2x + 6 - 5x + 10 = 3 $

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

Step 3: Subtract 16 from both sides:
$ -3x = 3 - 16 = -13 $

Step 4: Divide by -3:
$ x = \frac{-13}{-3} = \frac{13}{3} $

✔ Answer: $ x = \frac{13}{3} $ (≈ 4.333)

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

Step 1: Distribute:
$ 3x - 3 + 4x + 2 = 11 $

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

Step 3: Add 1 to both sides:
$ 7x = 12 $

Step 4: Divide by 7:
$ x = \frac{12}{7} $

✔ Answer: $ x = \frac{12}{7} $ (≈ 1.714)

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9. $ 2x - 1 = x + 5 $

Step 1: Subtract $ x $ from both sides:
$ 2x - x - 1 = 5 $
$ x - 1 = 5 $

Step 2: Add 1 to both sides:
$ x = 6 $

✔ Answer: $ x = 6 $

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

Step 1: Distribute:
$ 5x + 15 - 3x + 3 = 22 $

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

Step 3: Subtract 18 from both sides:
$ 2x = 4 $

Step 4: Divide by 2:
$ x = 2 $

✔ Answer: $ x = 2 $

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✔ Final Answers:

| Problem | Answer |
|--------|----------------|
| 1 | $ x = 6 $ |
| 2 | $ x = 9 $ |
| 3 | $ x = 18 $ |
| 4 | $ x = \frac{20}{11} $ |
| 5 | $ x = \frac{9}{5} $ |
| 6 | $ x = \frac{15}{11} $ |
| 7 | $ x = \frac{13}{3} $ |
| 8 | $ x = \frac{12}{7} $ |
| 9 | $ x = 6 $ |
| 10 | $ x = 2 $ |

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