Math Central: Solving Two-Step Equations - Free Printable

Let's solve each of these two-step equations step by step. The goal is to isolate the variable on one side of the equation.

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1. $ 3x + 7 = 25 $

Step 1: Subtract 7 from both sides:
$ 3x = 25 - 7 $
$ 3x = 18 $

Step 2: Divide both sides by 3:
$ x = \frac{18}{3} $
$ x = 6 $

✔ Answer: $ x = 6 $

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2. $ 0.5y + 4 = 7 $

Step 1: Subtract 4 from both sides:
$ 0.5y = 7 - 4 $
$ 0.5y = 3 $

Step 2: Divide both sides by 0.5 (or multiply by 2):
$ y = \frac{3}{0.5} = 6 $

✔ Answer: $ y = 6 $

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3. $ 8a - 6 = 34 $

Step 1: Add 6 to both sides:
$ 8a = 34 + 6 $
$ 8a = 40 $

Step 2: Divide both sides by 8:
$ a = \frac{40}{8} $
$ a = 5 $

✔ Answer: $ a = 5 $

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4. $ 16 = 4x - 8 $

Step 1: Add 8 to both sides:
$ 16 + 8 = 4x $
$ 24 = 4x $

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

✔ Answer: $ x = 6 $

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5. $ 3x + 7 + 2 = 33 $

Step 1: Combine like terms:
$ 3x + 9 = 33 $

Step 2: Subtract 9 from both sides:
$ 3x = 33 - 9 $
$ 3x = 24 $

Step 3: Divide by 3:
$ x = \frac{24}{3} $
$ x = 8 $

✔ Answer: $ x = 8 $

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6. $ 92 = 5y - 13 $

Step 1: Add 13 to both sides:
$ 92 + 13 = 5y $
$ 105 = 5y $

Step 2: Divide by 5:
$ y = \frac{105}{5} $
$ y = 21 $

✔ Answer: $ y = 21 $

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7. $ 5b + 2 + 13 = 90 $

Step 1: Combine like terms:
$ 5b + 15 = 90 $

Step 2: Subtract 15 from both sides:
$ 5b = 90 - 15 $
$ 5b = 75 $

Step 3: Divide by 5:
$ b = \frac{75}{5} $
$ b = 15 $

✔ Answer: $ b = 15 $

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8. $ 6c - 6 = 48 $

Step 1: Add 6 to both sides:
$ 6c = 48 + 6 $
$ 6c = 54 $

Step 2: Divide by 6:
$ c = \frac{54}{6} $
$ c = 9 $

✔ Answer: $ c = 9 $

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9. $ 12n - 12 = 72 $

Step 1: Add 12 to both sides:
$ 12n = 72 + 12 $
$ 12n = 84 $

Step 2: Divide by 12:
$ n = \frac{84}{12} $
$ n = 7 $

✔ Answer: $ n = 7 $

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✔ Final Answers:

1. $ x = 6 $
2. $ y = 6 $
3. $ a = 5 $
4. $ x = 6 $
5. $ x = 8 $
6. $ y = 21 $
7. $ b = 15 $
8. $ c = 9 $
9. $ n = 7 $

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