Algebraic equations practice worksheet with 12 linear equations for solving.

Let's solve each of these 12 linear equations step by step. We'll simplify both sides, isolate the variable $ x $, and find its value.

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1. $ x + 5 = 3(x + 1) $

Step 1: Expand the right side
$ x + 5 = 3x + 3 $

Step 2: Move all $ x $-terms to one side
$ x - 3x = 3 - 5 $
$ -2x = -2 $

Step 3: Solve for $ x $
$ x = \frac{-2}{-2} = 1 $

✔ Answer: $ x = 1 $

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2. $ 3(x + 5) = x + 1 $

Step 1: Expand left side
$ 3x + 15 = x + 1 $

Step 2: Move $ x $-terms to one side
$ 3x - x = 1 - 15 $
$ 2x = -14 $

Step 3: Solve
$ x = -7 $

✔ Answer: $ x = -7 $

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3. $ 3(x + 5) = 3(2x + 1) $

Step 1: Expand both sides
$ 3x + 15 = 6x + 3 $

Step 2: Move terms
$ 3x - 6x = 3 - 15 $
$ -3x = -12 $

Step 3: Solve
$ x = 4 $

✔ Answer: $ x = 4 $

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4. $ 3(x + 5) = 3(2x - 1) $

Step 1: Expand both sides
$ 3x + 15 = 6x - 3 $

Step 2: Move terms
$ 3x - 6x = -3 - 15 $
$ -3x = -18 $

Step 3: Solve
$ x = 6 $

✔ Answer: $ x = 6 $

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5. $ 3(x - 5) = 3(2x - 1) $

Step 1: Expand both sides
$ 3x - 15 = 6x - 3 $

Step 2: Move terms
$ 3x - 6x = -3 + 15 $
$ -3x = 12 $

Step 3: Solve
$ x = -4 $

✔ Answer: $ x = -4 $

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

Step 1: Expand both sides
$ 6x - 15 = 3x - 3 $

Step 2: Move terms
$ 6x - 3x = -3 + 15 $
$ 3x = 12 $

Step 3: Solve
$ x = 4 $

✔ Answer: $ x = 4 $

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7. $ 3(x - 5) = 3(2x + 1) $

Step 1: Expand both sides
$ 3x - 15 = 6x + 3 $

Step 2: Move terms
$ 3x - 6x = 3 + 15 $
$ -3x = 18 $

Step 3: Solve
$ x = -6 $

✔ Answer: $ x = -6 $

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8. $ 3(x - 5) = -3(2x + 1) $

Step 1: Expand both sides
$ 3x - 15 = -6x - 3 $

Step 2: Move terms
$ 3x + 6x = -3 + 15 $
$ 9x = 12 $

Step 3: Solve
$ x = \frac{12}{9} = \frac{4}{3} $

✔ Answer: $ x = \frac{4}{3} $

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9. $ -3(x + 5) = -3(2x + 1) $

Step 1: Expand both sides
$ -3x - 15 = -6x - 3 $

Step 2: Move terms
$ -3x + 6x = -3 + 15 $
$ 3x = 12 $

Step 3: Solve
$ x = 4 $

✔ Answer: $ x = 4 $

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10. $ -3(x - 5) = -3(2x + 1) $

Step 1: Expand both sides
$ -3x + 15 = -6x - 3 $

Step 2: Move terms
$ -3x + 6x = -3 - 15 $
$ 3x = -18 $

Step 3: Solve
$ x = -6 $

✔ Answer: $ x = -6 $

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11. $ -3(x - 5) = -3(2x - 1) $

Step 1: Expand both sides
$ -3x + 15 = -6x + 3 $

Step 2: Move terms
$ -3x + 6x = 3 - 15 $
$ 3x = -12 $

Step 3: Solve
$ x = -4 $

✔ Answer: $ x = -4 $

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12. $ -3(2x - 1) = -3(x - 5) $

Step 1: Expand both sides
$ -6x + 3 = -3x + 15 $

Step 2: Move terms
$ -6x + 3x = 15 - 3 $
$ -3x = 12 $

Step 3: Solve
$ x = -4 $

✔ Answer: $ x = -4 $

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✔ Final Answers:

| Problem | Solution |
|--------|----------|
| 1 | $ x = 1 $ |
| 2 | $ x = -7 $ |
| 3 | $ x = 4 $ |
| 4 | $ x = 6 $ |
| 5 | $ x = -4 $ |
| 6 | $ x = 4 $ |
| 7 | $ x = -6 $ |
| 8 | $ x = \frac{4}{3} $ |
| 9 | $ x = 4 $ |
| 10 | $ x = -6 $ |
| 11 | $ x = -4 $ |
| 12 | $ x = -4 $ |

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🔍 Observations:

- Some equations have identical solutions (e.g., #3, #6, #9 all give $ x = 4 $).
- Equations with same structure but opposite signs (like #8 vs #10) often yield different results.
- The key is always:
1. Distribute the constants.
2. Move variables to one side.
3. Solve for $ x $.

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