Math worksheet for solving addition and subtraction equations with variables.

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

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1. $ 12 - (y + 4) = 1 $

Step 1: Simplify the left side:
$$
12 - y - 4 = 1 \Rightarrow 8 - y = 1
$$

Step 2: Subtract 8 from both sides:
$$
-y = 1 - 8 = -7
$$

Step 3: Multiply both sides by -1:
$$
y = 7
$$

✔ Answer: $ y = 7 $

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2. $ 9 \cdot (7 + x + 5) = 56 $

Step 1: Simplify inside the parentheses:
$$
7 + x + 5 = x + 12
$$
So:
$$
9(x + 12) = 56
$$

Step 2: Divide both sides by 9:
$$
x + 12 = \frac{56}{9} \approx 6.22
$$

Wait — let’s check: $ 9 \times (x + 12) = 56 $

But $ 56 \div 9 = \frac{56}{9} $, which is not an integer. Let's keep it as a fraction.

$$
x + 12 = \frac{56}{9}
$$

Step 3: Subtract 12:
$$
x = \frac{56}{9} - 12 = \frac{56}{9} - \frac{108}{9} = \frac{-52}{9}
$$

✔ Answer: $ x = -\frac{52}{9} $

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3. $ (x + 6) + 5 = 2 $

Step 1: Combine like terms:
$$
x + 11 = 2
$$

Step 2: Subtract 11:
$$
x = 2 - 11 = -9
$$

✔ Answer: $ x = -9 $

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4. $ (y + 1) + 2 = 3 $

Step 1: Combine:
$$
y + 3 = 3
$$

Step 2: Subtract 3:
$$
y = 0
$$

✔ Answer: $ y = 0 $

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5. $ 10 \cdot (y + 11) = 1 $

Step 1: Divide both sides by 10:
$$
y + 11 = \frac{1}{10}
$$

Step 2: Subtract 11:
$$
y = \frac{1}{10} - 11 = \frac{1}{10} - \frac{110}{10} = -\frac{109}{10}
$$

✔ Answer: $ y = -\frac{109}{10} $ or $ -10.9 $

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6. $ 3 \cdot (10 + x + 12) = 95 $

Step 1: Simplify inside:
$$
10 + x + 12 = x + 22
$$
So:
$$
3(x + 22) = 95
$$

Step 2: Divide by 3:
$$
x + 22 = \frac{95}{3} \approx 31.67
$$

Step 3: Subtract 22:
$$
x = \frac{95}{3} - 22 = \frac{95}{3} - \frac{66}{3} = \frac{29}{3}
$$

✔ Answer: $ x = \frac{29}{3} $ or $ 9\frac{2}{3} $

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7. $ 4 - (y + 3) = 1 $

Step 1: Distribute the negative:
$$
4 - y - 3 = 1 \Rightarrow 1 - y = 1
$$

Step 2: Subtract 1:
$$
-y = 0 \Rightarrow y = 0
$$

✔ Answer: $ y = 0 $

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8. $ 3 \cdot (9 + y) = 36 $

Step 1: Divide both sides by 3:
$$
9 + y = 12
$$

Step 2: Subtract 9:
$$
y = 3
$$

✔ Answer: $ y = 3 $

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9. $ 9 + 7 \cdot y = 90 $

Step 1: Subtract 9:
$$
7y = 81
$$

Step 2: Divide by 7:
$$
y = \frac{81}{7} \approx 11.57
$$

✔ Answer: $ y = \frac{81}{7} $ or $ 11\frac{4}{7} $

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10. $ 6 \cdot (8 + x) = 90 $

Step 1: Divide both sides by 6:
$$
8 + x = 15
$$

Step 2: Subtract 8:
$$
x = 7
$$

✔ Answer: $ x = 7 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ y = 7 $ |
| 2 | $ x = -\frac{52}{9} $ |
| 3 | $ x = -9 $ |
| 4 | $ y = 0 $ |
| 5 | $ y = -\frac{109}{10} $ |
| 6 | $ x = \frac{29}{3} $ |
| 7 | $ y = 0 $ |
| 8 | $ y = 3 $ |
| 9 | $ y = \frac{81}{7} $ |
| 10 | $ x = 7 $ |

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