Solving Equations Practice 2 worksheet featuring 12 algebra problems for students to solve.

Here is the step-by-step solution to each of the 12 equations from the worksheet “Solving Equations Practice 2”. All work is shown as requested.

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1.
Equation:
\(\frac{x}{5} - 2 = 9\)

Step 1: Add 2 to both sides to isolate the fraction:
\(\frac{x}{5} = 9 + 2\)
\(\frac{x}{5} = 11\)

Step 2: Multiply both sides by 5:
\(x = 11 \times 5\)
\(\boxed{x = 55}\)

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2.
Equation:
\(\frac{x}{3} = -20\)

Step 1: Multiply both sides by 3:
\(x = -20 \times 3\)
\(\boxed{x = -60}\)

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3.
Equation:
\(-45 = 4x + 5x\)

Step 1: Combine like terms on the right:
\(-45 = 9x\)

Step 2: Divide both sides by 9:
\(x = \frac{-45}{9}\)
\(\boxed{x = -5}\)

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4.
Equation:
\(-8 - x = 11\)

Step 1: Add 8 to both sides:
\(-x = 11 + 8\)
\(-x = 19\)

Step 2: Multiply both sides by -1:
\(x = -19\)
\(\boxed{x = -19}\)

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5.
Equation:
\(\frac{x - 2}{6} = -4\)

Step 1: Multiply both sides by 6:
\(x - 2 = -4 \times 6\)
\(x - 2 = -24\)

Step 2: Add 2 to both sides:
\(x = -24 + 2\)
\(\boxed{x = -22}\)

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6.
Equation:
\(5 + \frac{x}{2} = 8\)

Step 1: Subtract 5 from both sides:
\(\frac{x}{2} = 8 - 5\)
\(\frac{x}{2} = 3\)

Step 2: Multiply both sides by 2:
\(x = 3 \times 2\)
\(\boxed{x = 6}\)

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7.
Equation:
\(\frac{x}{7} = 9\)

Step 1: Multiply both sides by 7:
\(x = 9 \times 7\)
\(\boxed{x = 63}\)

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8.
Equation:
\(24 + 4x = 6x\)

Step 1: Subtract 4x from both sides:
\(24 = 6x - 4x\)
\(24 = 2x\)

Step 2: Divide both sides by 2:
\(x = \frac{24}{2}\)
\(\boxed{x = 12}\)

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9.
Equation:
\(\frac{2}{5}x - 6 = 13\)

Step 1: Add 6 to both sides:
\(\frac{2}{5}x = 13 + 6\)
\(\frac{2}{5}x = 19\)

Step 2: Multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\):
\(x = 19 \times \frac{5}{2}\)
\(x = \frac{95}{2}\)
\(\boxed{x = 47.5}\) or \(\boxed{\frac{95}{2}}\)

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10.
Equation:
\(x + 15 = 74\)

Step 1: Subtract 15 from both sides:
\(x = 74 - 15\)
\(\boxed{x = 59}\)

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11.
Equation:
\(36 - x = 14\)

Step 1: Subtract 36 from both sides:
\(-x = 14 - 36\)
\(-x = -22\)

Step 2: Multiply both sides by -1:
\(x = 22\)
\(\boxed{x = 22}\)

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12.
Equation:
\(\frac{x + 6}{2} = 12\)

Step 1: Multiply both sides by 2:
\(x + 6 = 12 \times 2\)
\(x + 6 = 24\)

Step 2: Subtract 6 from both sides:
\(x = 24 - 6\)
\(\boxed{x = 18}\)

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✔ Final Answers Summary:

1. \(x = 55\)
2. \(x = -60\)
3. \(x = -5\)
4. \(x = -19\)
5. \(x = -22\)
6. \(x = 6\)
7. \(x = 63\)
8. \(x = 12\)
9. \(x = \frac{95}{2}\) or \(47.5\)
10. \(x = 59\)
11. \(x = 22\)
12. \(x = 18\)

All steps are shown and solutions are boxed for clarity. Let me know if you’d like these explained further!