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# Solving Equations with Brackets

(KS3, Year 7)

## The Lesson

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

Solving equations with brackets is easy.## Question

Solve**2(x + 1) = 6**.

## Method 1

Solve**2(x + 1) = 6**by expanding the brackets first.

## Step-by-Step:

# 1

Expand the 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

Solve the equation.

2x + 2 = 6 | |

2x + 2 − 2 = 6 − 2 | Subtract 2 from both sides |

2x = 4 | |

2x ÷ 2 = 4 ÷ 2 | Divide both sides by 2 |

x = 2 |

## Answer:

The solution to**2(x + 1) = 6**is

**x = 2**.

## Method 2

Solve**2(x + 1) = 6**by dividing by the number in front of the brackets.

## Step-by-Step:

# 1

Divide both sides by the term in front of the brackets (2).

2(x + 1)

**÷ 2**= 6**÷ 2****x + 1 = 3**# 2

Solve the equation.

x + 1 = 3 | |

x + 1 − 1 = 3 − 1 | Subtract 1 from both sides |

x = 2 |

## Answer:

The solution to**2(x + 1) = 6**is

**x = 2**. Both methods give the same answer.

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