Algebra worksheet featuring nine linear equations to solve for x, designed for educational practice.

Let's solve each equation step by step. These are all linear equations in one variable, and we'll solve for $ x $ using algebraic methods.

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1) $ 4x + 17 = 49 $

Step 1: Subtract 17 from both sides:
$ 4x = 49 - 17 $
$ 4x = 32 $

Step 2: Divide both sides by 4:
$ x = \frac{32}{4} $
$ x = 8 $

✔ Answer: $ x = 8 $

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2) $ 2x + 11 = 27 $

Step 1: Subtract 11 from both sides:
$ 2x = 27 - 11 $
$ 2x = 16 $

Step 2: Divide both sides by 2:
$ x = \frac{16}{2} $
$ x = 8 $

✔ Answer: $ x = 8 $

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3) $ 6x - 23 = 31 $

Step 1: Add 23 to both sides:
$ 6x = 31 + 23 $
$ 6x = 54 $

Step 2: Divide both sides by 6:
$ x = \frac{54}{6} $
$ x = 9 $

✔ Answer: $ x = 9 $

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4) $ 7x + 2 = 16 $

Step 1: Subtract 2 from both sides:
$ 7x = 16 - 2 $
$ 7x = 14 $

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

✔ Answer: $ x = 2 $

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5) $ 3x + 10 = 37 $

Step 1: Subtract 10 from both sides:
$ 3x = 37 - 10 $
$ 3x = 27 $

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

✔ Answer: $ x = 9 $

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6) $ 7x - 24 = 25 $

Step 1: Add 24 to both sides:
$ 7x = 25 + 24 $
$ 7x = 49 $

Step 2: Divide both sides by 7:
$ x = \frac{49}{7} $
$ x = 7 $

✔ Answer: $ x = 7 $

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7) $ 2x - 1 = 5 $

Step 1: Add 1 to both sides:
$ 2x = 5 + 1 $
$ 2x = 6 $

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

✔ Answer: $ x = 3 $

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8) $ 5x - 2 = 33 $

Step 1: Add 2 to both sides:
$ 5x = 33 + 2 $
$ 5x = 35 $

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

✔ Answer: $ x = 7 $

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9) $ 5x + 34 = 74 $

Step 1: Subtract 34 from both sides:
$ 5x = 74 - 34 $
$ 5x = 40 $

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

✔ Answer: $ x = 8 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $ x = 8 $ |
| 2) | $ x = 8 $ |
| 3) | $ x = 9 $ |
| 4) | $ x = 2 $ |
| 5) | $ x = 9 $ |
| 6) | $ x = 7 $ |
| 7) | $ x = 3 $ |
| 8) | $ x = 7 $ |
| 9) | $ x = 8 $ |

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🔍 Summary of Steps:

For each equation:
1. Isolate the term with $ x $ by moving constants to the other side.
2. Solve for $ x $ by dividing both sides by the coefficient of $ x $.

These are basic linear equations, and the key is performing the same operation on both sides to maintain balance.

Let me know if you'd like a visual explanation or help checking your work!