7.EE.B.4.A Worksheets - Common Core Math - Free Printable

Let's solve each of the two-step equations step by step. A two-step equation typically involves:

1. Isolating the variable term (using addition or subtraction).
2. Solving for the variable (using multiplication or division).

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1. $ 5x + 20 = 55 $

Step 1: Subtract 20 from both sides:
$ 5x = 55 - 20 $
$ 5x = 35 $

Step 2: Divide both sides by 5:
$ x = \frac{35}{5} $
$ x = 7 $

✔ Answer: $ x = 7 $

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2. $ -1x - 15 = 7 $

Step 1: Add 15 to both sides:
$ -x = 7 + 15 $
$ -x = 22 $

Step 2: Multiply both sides by -1:
$ x = -22 $

✔ Answer: $ x = -22 $

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3. $ -6x + 8 = -16 $

Step 1: Subtract 8 from both sides:
$ -6x = -16 - 8 $
$ -6x = -24 $

Step 2: Divide both sides by -6:
$ x = \frac{-24}{-6} $
$ x = 4 $

✔ Answer: $ x = 4 $

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4. $ 18 + 4x = 6 $

Step 1: Subtract 18 from both sides:
$ 4x = 6 - 18 $
$ 4x = -12 $

Step 2: Divide both sides by 4:
$ x = \frac{-12}{4} $
$ x = -3 $

✔ Answer: $ x = -3 $

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5. $ -7x - 9 = -23 $

Step 1: Add 9 to both sides:
$ -7x = -23 + 9 $
$ -7x = -14 $

Step 2: Divide both sides by -7:
$ x = \frac{-14}{-7} $
$ x = 2 $

✔ Answer: $ x = 2 $

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6. $ -9x + 12 = 15 $

Step 1: Subtract 12 from both sides:
$ -9x = 15 - 12 $
$ -9x = 3 $

Step 2: Divide both sides by -9:
$ x = \frac{3}{-9} $
$ x = -\frac{1}{3} $

✔ Answer: $ x = -\frac{1}{3} $

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7. $ 2(x + 10) = 60 $

Step 1: Distribute the 2:
$ 2x + 20 = 60 $

Step 2: Subtract 20 from both sides:
$ 2x = 40 $

Step 3: Divide by 2:
$ x = 20 $

✔ Answer: $ x = 20 $

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8. $ -6(x + 8) = -12 $

Step 1: Distribute the -6:
$ -6x - 48 = -12 $

Step 2: Add 48 to both sides:
$ -6x = -12 + 48 $
$ -6x = 36 $

Step 3: Divide by -6:
$ x = \frac{36}{-6} $
$ x = -6 $

✔ Answer: $ x = -6 $

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9. $ -3(x + 7) = 9 $

Step 1: Distribute the -3:
$ -3x - 21 = 9 $

Step 2: Add 21 to both sides:
$ -3x = 9 + 21 $
$ -3x = 30 $

Step 3: Divide by -3:
$ x = \frac{30}{-3} $
$ x = -10 $

✔ Answer: $ x = -10 $

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10. $ -2.4x + 8.6 = -10 $

Step 1: Subtract 8.6 from both sides:
$ -2.4x = -10 - 8.6 $
$ -2.4x = -18.6 $

Step 2: Divide by -2.4:
$ x = \frac{-18.6}{-2.4} $

To simplify:
Multiply numerator and denominator by 10 to eliminate decimals:
$ x = \frac{186}{24} $

Simplify: divide numerator and denominator by 6:
$ x = \frac{31}{4} = 7.75 $

✔ Answer: $ x = 7.75 $ or $ \frac{31}{4} $

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11. $ 2(x + \frac{1}{2}) = \frac{1}{2} $

Step 1: Distribute the 2:
$ 2x + 1 = \frac{1}{2} $

Step 2: Subtract 1 from both sides:
$ 2x = \frac{1}{2} - 1 $
$ 2x = -\frac{1}{2} $

Step 3: Divide by 2:
$ x = -\frac{1}{2} \div 2 = -\frac{1}{4} $

✔ Answer: $ x = -\frac{1}{4} $

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12. $ \frac{2}{3}(x + 3) = 6 $

Step 1: Multiply both sides by $ \frac{3}{2} $ to eliminate the fraction:
$ x + 3 = 6 \cdot \frac{3}{2} $
$ x + 3 = 9 $

Step 2: Subtract 3 from both sides:
$ x = 9 - 3 $
$ x = 6 $

✔ Answer: $ x = 6 $

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✔ Final Answers:

| Problem | Answer |
|--------|----------------|
| 1 | $ x = 7 $ |
| 2 | $ x = -22 $ |
| 3 | $ x = 4 $ |
| 4 | $ x = -3 $ |
| 5 | $ x = 2 $ |
| 6 | $ x = -\frac{1}{3} $ |
| 7 | $ x = 20 $ |
| 8 | $ x = -6 $ |
| 9 | $ x = -10 $ |
| 10 | $ x = 7.75 $ or $ \frac{31}{4} $ |
| 11 | $ x = -\frac{1}{4} $ |
| 12 | $ x = 6 $ |

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