Printable worksheet featuring 12 linear equation problems designed to help students practice isolating variables.

Let's solve each equation step by step from the Linear Equations Worksheet.

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1 a. $ 8 = \frac{z}{6} $

To solve for $ z $, multiply both sides by 6:

$$
8 \times 6 = z \Rightarrow z = 48
$$

✔ Answer: $ z = 48 $

---

1 b. $ c + 1 = 1 $

Subtract 1 from both sides:

$$
c = 1 - 1 \Rightarrow c = 0
$$

✔ Answer: $ c = 0 $

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2 a. $ 11 = \frac{x}{8} $

Multiply both sides by 8:

$$
11 \times 8 = x \Rightarrow x = 88
$$

✔ Answer: $ x = 88 $

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2 b. $ 2 + y = 11 $

Subtract 2 from both sides:

$$
y = 11 - 2 \Rightarrow y = 9
$$

✔ Answer: $ y = 9 $

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3 a. $ b - 11 = 11 $

Add 11 to both sides:

$$
b = 11 + 11 \Rightarrow b = 22
$$

✔ Answer: $ b = 22 $

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3 b. $ c + 5 = 5 $

Subtract 5 from both sides:

$$
c = 5 - 5 \Rightarrow c = 0
$$

✔ Answer: $ c = 0 $

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4 a. $ 5z = 4 $

Divide both sides by 5:

$$
z = \frac{4}{5}
$$

✔ Answer: $ z = \frac{4}{5} $

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4 b. $ 5 - b = 1 $

Subtract 5 from both sides:

$$
-b = 1 - 5 \Rightarrow -b = -4
$$

Multiply both sides by -1:

$$
b = 4
$$

✔ Answer: $ b = 4 $

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5 a. $ 5 = 9s $

Divide both sides by 9:

$$
s = \frac{5}{9}
$$

✔ Answer: $ s = \frac{5}{9} $

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5 b. $ 3 = 7p $

Divide both sides by 7:

$$
p = \frac{3}{7}
$$

✔ Answer: $ p = \frac{3}{7} $

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6 a. $ 11 = p + 1 $

Subtract 1 from both sides:

$$
p = 11 - 1 \Rightarrow p = 10
$$

✔ Answer: $ p = 10 $

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6 b. $ \frac{c}{11} = 2 $

Multiply both sides by 11:

$$
c = 2 \times 11 \Rightarrow c = 22
$$

✔ Answer: $ c = 22 $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 a | $ z = 48 $ |
| 1 b | $ c = 0 $ |
| 2 a | $ x = 88 $ |
| 2 b | $ y = 9 $ |
| 3 a | $ b = 22 $ |
| 3 b | $ c = 0 $ |
| 4 a | $ z = \frac{4}{5} $ |
| 4 b | $ b = 4 $ |
| 5 a | $ s = \frac{5}{9} $ |
| 5 b | $ p = \frac{3}{7} $ |
| 6 a | $ p = 10 $ |
| 6 b | $ c = 22 $ |

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