Worksheet for solving linear equations with 10 problems involving variables and constants.

Let's solve each of the linear equations step by step. The goal is to isolate the variable (x or y) on one side of the equation.

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1. $ 7x + 9 = 23 $

Step 1: Subtract 9 from both sides
$ 7x = 23 - 9 $
$ 7x = 14 $

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

✔ Answer: $ x = 2 $

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2. $ 4x + 17 = 18 $

Step 1: Subtract 17 from both sides
$ 4x = 18 - 17 $
$ 4x = 1 $

Step 2: Divide both sides by 4
$ x = \frac{1}{4} $

✔ Answer: $ x = \frac{1}{4} $

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3. $ 9y + 5 = 41 $

Step 1: Subtract 5 from both sides
$ 9y = 41 - 5 $
$ 9y = 36 $

Step 2: Divide both sides by 9
$ y = \frac{36}{9} = 4 $

✔ Answer: $ y = 4 $

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4. $ 15x + 6 = 51 $

Step 1: Subtract 6 from both sides
$ 15x = 51 - 6 $
$ 15x = 45 $

Step 2: Divide both sides by 15
$ x = \frac{45}{15} = 3 $

✔ Answer: $ x = 3 $

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5. $ 12y + 9 = 69 $

Step 1: Subtract 9 from both sides
$ 12y = 69 - 9 $
$ 12y = 60 $

Step 2: Divide both sides by 12
$ y = \frac{60}{12} = 5 $

✔ Answer: $ y = 5 $

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6. $ 10y + 2 = 72 $

Step 1: Subtract 2 from both sides
$ 10y = 72 - 2 $
$ 10y = 70 $

Step 2: Divide both sides by 10
$ y = \frac{70}{10} = 7 $

✔ Answer: $ y = 7 $

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7. $ 6x + 8 = 32 $

Step 1: Subtract 8 from both sides
$ 6x = 32 - 8 $
$ 6x = 24 $

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

✔ Answer: $ x = 4 $

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8. $ 13x + 3 = 29 $

Step 1: Subtract 3 from both sides
$ 13x = 29 - 3 $
$ 13x = 26 $

Step 2: Divide both sides by 13
$ x = \frac{26}{13} = 2 $

✔ Answer: $ x = 2 $

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9. $ 4y + 7 = 19 $

Step 1: Subtract 7 from both sides
$ 4y = 19 - 7 $
$ 4y = 12 $

Step 2: Divide both sides by 4
$ y = \frac{12}{4} = 3 $

✔ Answer: $ y = 3 $

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10. $ 9y + 6 = 24 $

Step 1: Subtract 6 from both sides
$ 9y = 24 - 6 $
$ 9y = 18 $

Step 2: Divide both sides by 9
$ y = \frac{18}{9} = 2 $

✔ Answer: $ y = 2 $

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11. $ 8x + 8 = 48 $

Step 1: Subtract 8 from both sides
$ 8x = 48 - 8 $
$ 8x = 40 $

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

✔ Answer: $ x = 5 $

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12. $ 5x + 7 = 37 $

Step 1: Subtract 7 from both sides
$ 5x = 37 - 7 $
$ 5x = 30 $

Step 2: Divide both sides by 5
$ x = \frac{30}{5} = 6 $

✔ Answer: $ x = 6 $

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✔ Final Answers:

| Equation | Solution |
|--------|---------|
| $ 7x + 9 = 23 $ | $ x = 2 $ |
| $ 4x + 17 = 18 $ | $ x = \frac{1}{4} $ |
| $ 9y + 5 = 41 $ | $ y = 4 $ |
| $ 15x + 6 = 51 $ | $ x = 3 $ |
| $ 12y + 9 = 69 $ | $ y = 5 $ |
| $ 10y + 2 = 72 $ | $ y = 7 $ |
| $ 6x + 8 = 32 $ | $ x = 4 $ |
| $ 13x + 3 = 29 $ | $ x = 2 $ |
| $ 4y + 7 = 19 $ | $ y = 3 $ |
| $ 9y + 6 = 24 $ | $ y = 2 $ |
| $ 8x + 8 = 48 $ | $ x = 5 $ |
| $ 5x + 7 = 37 $ | $ x = 6 $ |

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🔍 Summary of Steps:

To solve any linear equation like $ ax + b = c $:
1. Subtract $ b $ from both sides → $ ax = c - b $
2. Divide both sides by $ a $ → $ x = \frac{c - b}{a} $

This method works for all similar equations.

Let me know if you'd like this in printable format or with extra explanation!