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# Solving Equations with Two Sets of Brackets

(KS3, Year 8)

## The Lesson

We can solve equations with two sets of brackets. Imagine we wanted to solve the equation shown below.## How to Solve Equations with Two Sets of Brackets

Solving equations with two sets of brackets is easy.## Question

Solve**2(x + 1) + 3(x − 4) = 0**.

## Step-by-Step:

# 1

Expand the first set of brackets on the left-hand side of the equation.

2(x + 1) = 2 × x + 2 × 1

**2x + 2****Don't forget:**Expand the brackets by multiplying each term inside the brackets with the term outside of it.# 2

Expand the second set of brackets on the left-hand side of the equation, having replaced the first set of brackets with the result of

**Step 1**.
3(x − 4) = 3 × x − 3 × 4

**3x − 12**# 3

Collect like terms.

- Identify the like terms. The like
**x**terms are 2x and 3x. The like**number**terms are 2 and −12.

- Collect the like
**x**terms and the like**number**terms together

# 4

Solve the equation.

5x − 10 = 0 | |

5x − 10 + 10 = 0 + 10 |
Add 10 to both sides |

5x = 10 | |

5x ÷ 5 = 10 ÷ 5 |
Divide both sides by 5 |

x = 2 |

## Answer:

The solution to**2(x + 1) + 3(x − 4) = 0**is

**x = 2**.

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