Worksheet for solving linear equations with ten practice problems.

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

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1. $7x + 9 = 23$

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

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:
$4x = 18 - 17 = 1$

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

✔ Answer: $x = \frac{1}{4}$

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3. $9y + 5 = 41$

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

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

✔ Answer: $y = 4$

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4. $15x + 6 = 51$

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

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

✔ Answer: $x = 3$

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5. $12y + 9 = 69$

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

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

✔ Answer: $y = 5$

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6. $10y + 2 = 72$

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

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

✔ Answer: $y = 7$

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7. $6x + 8 = 32$

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

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

✔ Answer: $x = 4$

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8. $13x + 3 = 29$

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

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

✔ Answer: $x = 2$

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9. $4y + 7 = 19$

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

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

✔ Answer: $y = 3$

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10. $9y + 6 = 24$

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

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

✔ Answer: $y = 2$

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11. $8x + 8 = 48$

Step 1: Subtract 8:
$8x = 48 - 8 = 40$

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

✔ Answer: $x = 5$

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12. $5x + 7 = 37$

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

Step 2: Divide 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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🔍 Explanation of Method:

To solve a linear equation like $ax + b = c$, follow these steps:
1. Subtract $b$ from both sides to isolate the term with the variable.
2. Divide by $a$ to solve for the variable.

This method works because we are using inverse operations to undo what is being done to the variable, keeping the equation balanced.

Let me know if you'd like this formatted as a printable answer key!