Year 9 Maths Worksheets | Printable Maths worksheets - Free Printable

Let's solve each equation step-by-step and provide the answers. The goal is to isolate the variable $ x $ on one side of the equation.

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Section A: Basic Linear Equations

#### 1) $ 4x + 10 = 30 $
- Subtract 10 from both sides:
$ 4x = 20 $
- Divide by 4:
$ x = 5 $

✔ Answer: $ x = 5 $

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#### 2) $ 4x - 8 = 20 $
- Add 8 to both sides:
$ 4x = 28 $
- Divide by 4:
$ x = 7 $

✔ Answer: $ x = 7 $

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#### 3) $ 5 + 2x = 65 $
- Subtract 5:
$ 2x = 60 $
- Divide by 2:
$ x = 30 $

✔ Answer: $ x = 30 $

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#### 4) $ 9 + 4x = -15 $
- Subtract 9:
$ 4x = -24 $
- Divide by 4:
$ x = -6 $

✔ Answer: $ x = -6 $

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#### 5) $ 14 + 6x = 2 $
- Subtract 14:
$ 6x = -12 $
- Divide by 6:
$ x = -2 $

✔ Answer: $ x = -2 $

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#### 6) $ 2x - 3 = -2 $
- Add 3:
$ 2x = 1 $
- Divide by 2:
$ x = \frac{1}{2} $

✔ Answer: $ x = \frac{1}{2} $

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#### 7) $ 5 + 10x = -15 $
- Subtract 5:
$ 10x = -20 $
- Divide by 10:
$ x = -2 $

✔ Answer: $ x = -2 $

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#### 8) $ 10 = 7 - x $
- Subtract 7:
$ 3 = -x $
- Multiply both sides by -1:
$ x = -3 $

✔ Answer: $ x = -3 $

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#### 9) $ -3 = 16 - x $
- Subtract 16:
$ -19 = -x $
- Multiply by -1:
$ x = 19 $

✔ Answer: $ x = 19 $

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

✔ Answer: $ x = 8 $

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#### 11) $ 25 = 46 - 3x $
- Subtract 46:
$ -21 = -3x $
- Divide by -3:
$ x = 7 $

✔ Answer: $ x = 7 $

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#### 12) $ 8 = 9 - 5x $
- Subtract 9:
$ -1 = -5x $
- Divide by -5:
$ x = \frac{1}{5} $

✔ Answer: $ x = \frac{1}{5} $

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Section B: Equations with Fractions

#### 1) $ \frac{x}{2} + 11 = 19 $
- Subtract 11:
$ \frac{x}{2} = 8 $
- Multiply by 2:
$ x = 16 $

✔ Answer: $ x = 16 $

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#### 2) $ \frac{x}{7} - 6 = 1 $
- Add 6:
$ \frac{x}{7} = 7 $
- Multiply by 7:
$ x = 49 $

✔ Answer: $ x = 49 $

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#### 3) $ 12 + \frac{x}{5} = 20 $
- Subtract 12:
$ \frac{x}{5} = 8 $
- Multiply by 5:
$ x = 40 $

✔ Answer: $ x = 40 $

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#### 4) $ 3 = \frac{x}{4} - 3 $
- Add 3:
$ 6 = \frac{x}{4} $
- Multiply by 4:
$ x = 24 $

✔ Answer: $ x = 24 $

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#### 5) $ 7 = \frac{x}{2} - 4 $
- Add 4:
$ 11 = \frac{x}{2} $
- Multiply by 2:
$ x = 22 $

✔ Answer: $ x = 22 $

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#### 6) $ -2 = \frac{x}{8} - 5 $
- Add 5:
$ 3 = \frac{x}{8} $
- Multiply by 8:
$ x = 24 $

✔ Answer: $ x = 24 $

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#### 7) $ -1 = 6 + \frac{x}{2} $
- Subtract 6:
$ -7 = \frac{x}{2} $
- Multiply by 2:
$ x = -14 $

✔ Answer: $ x = -14 $

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#### 8) $ 14 - \frac{x}{3} = 10 $
- Subtract 14:
$ -\frac{x}{3} = -4 $
- Multiply by -3:
$ x = 12 $

✔ Answer: $ x = 12 $

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#### 9) $ 5 - \frac{x}{9} = -1 $
- Subtract 5:
$ -\frac{x}{9} = -6 $
- Multiply by -9:
$ x = 54 $

✔ Answer: $ x = 54 $

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#### 10) $ \frac{x + 5}{3} = 12 $
- Multiply both sides by 3:
$ x + 5 = 36 $
- Subtract 5:
$ x = 31 $

✔ Answer: $ x = 31 $

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#### 11) $ \frac{x - 4}{11} = 9 $
- Multiply by 11:
$ x - 4 = 99 $
- Add 4:
$ x = 103 $

✔ Answer: $ x = 103 $

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#### 12) $ \frac{x + 3}{8} = -2 $
- Multiply by 8:
$ x + 3 = -16 $
- Subtract 3:
$ x = -19 $

✔ Answer: $ x = -19 $

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Section C: Equations with Brackets

#### 1) $ 3(x + 2) = 15 $
- Expand:
$ 3x + 6 = 15 $
- Subtract 6:
$ 3x = 9 $
- Divide by 3:
$ x = 3 $

✔ Answer: $ x = 3 $

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#### 2) $ 2(x + 5) = 24 $
- Expand:
$ 2x + 10 = 24 $
- Subtract 10:
$ 2x = 14 $
- Divide by 2:
$ x = 7 $

✔ Answer: $ x = 7 $

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#### 3) $ 6(x - 9) = 12 $
- Expand:
$ 6x - 54 = 12 $
- Add 54:
$ 6x = 66 $
- Divide by 6:
$ x = 11 $

✔ Answer: $ x = 11 $

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#### 4) $ 2(3x + 5) = -44 $
- Expand:
$ 6x + 10 = -44 $
- Subtract 10:
$ 6x = -54 $
- Divide by 6:
$ x = -9 $

✔ Answer: $ x = -9 $

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#### 5) $ 5(4x - 3) = 11 $
- Expand:
$ 20x - 15 = 11 $
- Add 15:
$ 20x = 26 $
- Divide by 20:
$ x = \frac{26}{20} = \frac{13}{10} = 1.3 $

✔ Answer: $ x = \frac{13}{10} $ or $ 1.3 $

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#### 6) $ -3(2x + 1) = 21 $
- Expand:
$ -6x - 3 = 21 $
- Add 3:
$ -6x = 24 $
- Divide by -6:
$ x = -4 $

✔ Answer: $ x = -4 $

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#### 7) $ -9(x - 4) = 54 $
- Expand:
$ -9x + 36 = 54 $
- Subtract 36:
$ -9x = 18 $
- Divide by -9:
$ x = -2 $

✔ Answer: $ x = -2 $

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#### 8) $ 7(x - 4) - 3 = 46 $
- Expand:
$ 7x - 28 - 3 = 46 $
- Simplify:
$ 7x - 31 = 46 $
- Add 31:
$ 7x = 77 $
- Divide by 7:
$ x = 11 $

✔ Answer: $ x = 11 $

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#### 9) $ 2(3x - 1) + 3 = 21 $
- Expand:
$ 6x - 2 + 3 = 21 $
- Simplify:
$ 6x + 1 = 21 $
- Subtract 1:
$ 6x = 20 $
- Divide by 6:
$ x = \frac{20}{6} = \frac{10}{3} \approx 3.33 $

✔ Answer: $ x = \frac{10}{3} $

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#### 10) $ 2(x + 1) + 3x = 37 $
- Expand:
$ 2x + 2 + 3x = 37 $
- Combine like terms:
$ 5x + 2 = 37 $
- Subtract 2:
$ 5x = 35 $
- Divide by 5:
$ x = 7 $

✔ Answer: $ x = 7 $

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#### 11) $ 12 + 4(2x + 4) = 68 $
- Expand:
$ 12 + 8x + 16 = 68 $
- Combine:
$ 8x + 28 = 68 $
- Subtract 28:
$ 8x = 40 $
- Divide by 8:
$ x = 5 $

✔ Answer: $ x = 5 $

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#### 12) $ 3x - 2(6x - 3) = 42 $
- Expand:
$ 3x - 12x + 6 = 42 $
- Combine:
$ -9x + 6 = 42 $
- Subtract 6:
$ -9x = 36 $
- Divide by -9:
$ x = -4 $

✔ Answer: $ x = -4 $

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✔ Final Answers Summary

#### Section A
1. $ x = 5 $
2. $ x = 7 $
3. $ x = 30 $
4. $ x = -6 $
5. $ x = -2 $
6. $ x = \frac{1}{2} $
7. $ x = -2 $
8. $ x = -3 $
9. $ x = 19 $
10. $ x = 8 $
11. $ x = 7 $
12. $ x = \frac{1}{5} $

#### Section B
1. $ x = 16 $
2. $ x = 49 $
3. $ x = 40 $
4. $ x = 24 $
5. $ x = 22 $
6. $ x = 24 $
7. $ x = -14 $
8. $ x = 12 $
9. $ x = 54 $
10. $ x = 31 $
11. $ x = 103 $
12. $ x = -19 $

#### Section C
1. $ x = 3 $
2. $ x = 7 $
3. $ x = 11 $
4. $ x = -9 $
5. $ x = \frac{13}{10} $
6. $ x = -4 $
7. $ x = -2 $
8. $ x = 11 $
9. $ x = \frac{10}{3} $
10. $ x = 7 $
11. $ x = 5 $
12. $ x = -4 $

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