Challenge your algebra skills by solving for x in these two-step equations.

Let's solve each of these two-step equations step by step. These equations involve fractions, so we'll carefully isolate the variable $ x $ using inverse operations.

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1. $ \frac{3}{4}x + 6 = 15 $

Step 1: Subtract 6 from both sides:
$$
\frac{3}{4}x = 15 - 6 = 9
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{3}{4} $, which is $ \frac{4}{3} $:
$$
x = 9 \cdot \frac{4}{3} = \frac{36}{3} = 12
$$

✔ Answer: $ x = 12 $

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2. $ \frac{2}{3}x - 4 = 1 $

Step 1: Add 4 to both sides:
$$
\frac{2}{3}x = 1 + 4 = 5
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{2}{3} $, which is $ \frac{3}{2} $:
$$
x = 5 \cdot \frac{3}{2} = \frac{15}{2} = 7.5
$$

✔ Answer: $ x = \frac{15}{2} $ or $ 7.5 $

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3. $ \frac{5}{6}x - 10 = 5 $

Step 1: Add 10 to both sides:
$$
\frac{5}{6}x = 5 + 10 = 15
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{5}{6} $, which is $ \frac{6}{5} $:
$$
x = 15 \cdot \frac{6}{5} = \frac{90}{5} = 18
$$

✔ Answer: $ x = 18 $

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4. $ 10 = \frac{2}{5}x - 8 $

Step 1: Add 8 to both sides:
$$
10 + 8 = \frac{2}{5}x \Rightarrow 18 = \frac{2}{5}x
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{2}{5} $, which is $ \frac{5}{2} $:
$$
x = 18 \cdot \frac{5}{2} = \frac{90}{2} = 45
$$

✔ Answer: $ x = 45 $

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5. $ \frac{4}{5}x - 2 = 2 $

Step 1: Add 2 to both sides:
$$
\frac{4}{5}x = 2 + 2 = 4
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{4}{5} $, which is $ \frac{5}{4} $:
$$
x = 4 \cdot \frac{5}{4} = 5
$$

✔ Answer: $ x = 5 $

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6. $ 6 = \frac{2}{3}x - 3 $

Step 1: Add 3 to both sides:
$$
6 + 3 = \frac{2}{3}x \Rightarrow 9 = \frac{2}{3}x
$$

Step 2: Multiply both sides by $ \frac{3}{2} $:
$$
x = 9 \cdot \frac{3}{2} = \frac{27}{2} = 13.5
$$

✔ Answer: $ x = \frac{27}{2} $ or $ 13.5 $

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7. $ 6 + \frac{7}{2}x = 13 $

Step 1: Subtract 6 from both sides:
$$
\frac{7}{2}x = 13 - 6 = 7
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{7}{2} $, which is $ \frac{2}{7} $:
$$
x = 7 \cdot \frac{2}{7} = 2
$$

✔ Answer: $ x = 2 $

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8. $ \frac{7}{8}x - 6 = 8 $

Step 1: Add 6 to both sides:
$$
\frac{7}{8}x = 8 + 6 = 14
$$

Step 2: Multiply both sides by the reciprocal of $ \frac{7}{8} $, which is $ \frac{8}{7} $:
$$
x = 14 \cdot \frac{8}{7} = \frac{112}{7} = 16
$$

✔ Answer: $ x = 16 $

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✔ Final Answers:

| Equation | Solution |
|--------|---------|
| $ \frac{3}{4}x + 6 = 15 $ | $ x = 12 $ |
| $ \frac{2}{3}x - 4 = 1 $ | $ x = \frac{15}{2} $ or $ 7.5 $ |
| $ \frac{5}{6}x - 10 = 5 $ | $ x = 18 $ |
| $ 10 = \frac{2}{5}x - 8 $ | $ x = 45 $ |
| $ \frac{4}{5}x - 2 = 2 $ | $ x = 5 $ |
| $ 6 = \frac{2}{3}x - 3 $ | $ x = \frac{27}{2} $ or $ 13.5 $ |
| $ 6 + \frac{7}{2}x = 13 $ | $ x = 2 $ |
| $ \frac{7}{8}x - 6 = 8 $ | $ x = 16 $ |

Let me know if you'd like these checked with substitution!