Math worksheet for solving equations involving brackets, divided into Section A and Section B, designed for algebra practice.

Let's solve each equation step-by-step, following the instructions: expand the brackets and then solve for $ x $.

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Section A

#### 1) $ 3(x + 6) = 27 $
- Expand: $ 3x + 18 = 27 $
- Subtract 18: $ 3x = 9 $
- Divide by 3: $ x = 3 $

✔ Answer: $ x = 3 $

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#### 2) $ 2(x + 4) = 22 $
- Expand: $ 2x + 8 = 22 $
- Subtract 8: $ 2x = 14 $
- Divide by 2: $ x = 7 $

✔ Answer: $ x = 7 $

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#### 3) $ 6(x - 5) = 42 $
- Expand: $ 6x - 30 = 42 $
- Add 30: $ 6x = 72 $
- Divide by 6: $ x = 12 $

✔ Answer: $ x = 12 $

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#### 4) $ 2(x - 3) = 16 $
- Expand: $ 2x - 6 = 16 $
- Add 6: $ 2x = 22 $
- Divide by 2: $ x = 11 $

✔ Answer: $ x = 11 $

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#### 5) $ 4(2x + 5) = 36 $
- Expand: $ 8x + 20 = 36 $
- Subtract 20: $ 8x = 16 $
- Divide by 8: $ x = 2 $

✔ Answer: $ x = 2 $

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#### 6) $ 8(3x - 2) = 80 $
- Expand: $ 24x - 16 = 80 $
- Add 16: $ 24x = 96 $
- Divide by 24: $ x = 4 $

✔ Answer: $ x = 4 $

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#### 7) $ 3(6x - 7) = 15 $
- Expand: $ 18x - 21 = 15 $
- Add 21: $ 18x = 36 $
- Divide by 18: $ x = 2 $

✔ Answer: $ x = 2 $

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#### 8) $ 9(7x + 1) = 72 $
- Expand: $ 63x + 9 = 72 $
- Subtract 9: $ 63x = 63 $
- Divide by 63: $ x = 1 $

✔ Answer: $ x = 1 $

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#### 9) $ 4(3x + 5) = 8 $
- Expand: $ 12x + 20 = 8 $
- Subtract 20: $ 12x = -12 $
- Divide by 12: $ x = -1 $

✔ Answer: $ x = -1 $

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#### 10) $ 2(4x + 2) = -12 $
- Expand: $ 8x + 4 = -12 $
- Subtract 4: $ 8x = -16 $
- Divide by 8: $ x = -2 $

✔ Answer: $ x = -2 $

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#### 11) $ 10(3x - 1) = -100 $
- Expand: $ 30x - 10 = -100 $
- Add 10: $ 30x = -90 $
- Divide by 30: $ x = -3 $

✔ Answer: $ x = -3 $

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#### 12) $ 12(2x + 7) = 96 $
- Expand: $ 24x + 84 = 96 $
- Subtract 84: $ 24x = 12 $
- Divide by 24: $ x = \frac{1}{2} $

✔ Answer: $ x = \frac{1}{2} $

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Section B

Now we deal with fractions. We'll eliminate denominators first, then expand and solve.

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#### 1) $ \frac{x + 8}{2} = 9 $
- Multiply both sides by 2: $ x + 8 = 18 $
- Subtract 8: $ x = 10 $

✔ Answer: $ x = 10 $

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#### 2) $ \frac{x + 6}{5} = 7 $
- Multiply both sides by 5: $ x + 6 = 35 $
- Subtract 6: $ x = 29 $

✔ Answer: $ x = 29 $

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#### 3) $ \frac{2x + 5}{3} = 9 $
- Multiply both sides by 3: $ 2x + 5 = 27 $
- Subtract 5: $ 2x = 22 $
- Divide by 2: $ x = 11 $

✔ Answer: $ x = 11 $

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#### 4) $ \frac{6(7x + 2)}{9} = 6 $
- Simplify left side: $ \frac{42x + 12}{9} = 6 $
- Multiply both sides by 9: $ 42x + 12 = 54 $
- Subtract 12: $ 42x = 42 $
- Divide by 42: $ x = 1 $

✔ Answer: $ x = 1 $

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#### 5) $ \frac{2(3x + 4)}{7} = -4 $
- Simplify numerator: $ \frac{6x + 8}{7} = -4 $
- Multiply both sides by 7: $ 6x + 8 = -28 $
- Subtract 8: $ 6x = -36 $
- Divide by 6: $ x = -6 $

✔ Answer: $ x = -6 $

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#### 6) $ \frac{3(4x - 6)}{9} = -6 $
- Simplify numerator: $ \frac{12x - 18}{9} = -6 $
- Multiply both sides by 9: $ 12x - 18 = -54 $
- Add 18: $ 12x = -36 $
- Divide by 12: $ x = -3 $

✔ Answer: $ x = -3 $

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#### 7) $ \frac{1}{2}(4x + 6) = 9 $
- Multiply both sides by 2: $ 4x + 6 = 18 $
- Subtract 6: $ 4x = 12 $
- Divide by 4: $ x = 3 $

✔ Answer: $ x = 3 $

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#### 8) $ \frac{1}{2}(2x + 12) = 1 $
- Multiply both sides by 2: $ 2x + 12 = 2 $
- Subtract 12: $ 2x = -10 $
- Divide by 2: $ x = -5 $

✔ Answer: $ x = -5 $

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#### 9) $ \frac{1}{2}(3x + 5) = 13 $
- Multiply both sides by 2: $ 3x + 5 = 26 $
- Subtract 5: $ 3x = 21 $
- Divide by 3: $ x = 7 $

✔ Answer: $ x = 7 $

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✔ Final Answers Summary:

#### Section A
1) $ x = 3 $
2) $ x = 7 $
3) $ x = 12 $
4) $ x = 11 $
5) $ x = 2 $
6) $ x = 4 $
7) $ x = 2 $
8) $ x = 1 $
9) $ x = -1 $
10) $ x = -2 $
11) $ x = -3 $
12) $ x = \frac{1}{2} $

#### Section B
1) $ x = 10 $
2) $ x = 29 $
3) $ x = 11 $
4) $ x = 1 $
5) $ x = -6 $
6) $ x = -3 $
7) $ x = 3 $
8) $ x = -5 $
9) $ x = 7 $

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