Solving equations with brackets worksheet - Free Printable

We are given 6 algebraic equations to solve by expanding the brackets first, then solving for `x`.

Let’s go one by one.

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1. 2(x + 3) = 18

Step 1: Expand the bracket
Multiply 2 by each term inside the bracket:
> 2 × x = 2x
> 2 × 3 = 6
So:
2x + 6 = 18

Step 2: Subtract 6 from both sides
> 2x = 18 - 6
> 2x = 12

Step 3: Divide both sides by 2
> x = 12 ÷ 2
> x = 6

✔ Answer: x = 6

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2. 3(x - 3) = 12

Step 1: Expand the bracket
> 3 × x = 3x
> 3 × (-3) = -9
So:
3x - 9 = 12

Step 2: Add 9 to both sides
> 3x = 12 + 9
> 3x = 21

Step 3: Divide both sides by 3
> x = 21 ÷ 3
> x = 7

✔ Answer: x = 7

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3. 6(3x + 1) = 168

Step 1: Expand the bracket
> 6 × 3x = 18x
> 6 × 1 = 6
So:
18x + 6 = 168

Step 2: Subtract 6 from both sides
> 18x = 168 - 6
> 18x = 162

Step 3: Divide both sides by 18
> x = 162 ÷ 18
> x = 9

✔ Answer: x = 9

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4. 7(x - 2) = 42

Step 1: Expand the bracket
> 7 × x = 7x
> 7 × (-2) = -14
So:
7x - 14 = 42

Step 2: Add 14 to both sides
> 7x = 42 + 14
> 7x = 56

Step 3: Divide both sides by 7
> x = 56 ÷ 7
> x = 8

✔ Answer: x = 8

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5. 3(6x + 2) = 60

Step 1: Expand the bracket
> 3 × 6x = 18x
> 3 × 2 = 6
So:
18x + 6 = 60

Step 2: Subtract 6 from both sides
> 18x = 60 - 6
> 18x = 54

Step 3: Divide both sides by 18
> x = 54 ÷ 18
> x = 3

✔ Answer: x = 3

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6. 2(3x - 5) = 14

Step 1: Expand the bracket
> 2 × 3x = 6x
> 2 × (-5) = -10
So:
6x - 10 = 14

Step 2: Add 10 to both sides
> 6x = 14 + 10
> 6x = 24

Step 3: Divide both sides by 6
> x = 24 ÷ 6
> x = 4

✔ Answer: x = 4

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## ✔ Final Answers:

1. x = 6
2. x = 7
3. x = 9
4. x = 8
5. x = 3
6. x = 4

All solved by expanding brackets and isolating `x` using inverse operations.