Equations with brackets

The Maths Habit

  1. Solve 6x + 5 = 47

    x = 7

  2. Solve 2x − 9 = 6

    x = 7.5

  3. Solve 5x + 20 = 5

    x = −3

Ben works out 3 × (2 + 4)
and gets 10.
What did he do wrong?

He only multiplied the 2: 3 × 6 = 18

Expand

  1. 3(x + 4)

    3x + 12

  2. 5(x − 2)

    5x − 10

  3. 3(2x − 5)

    6x − 15

  4. 4(2x + 3)

    8x + 12

What is the first step?

4(x + 1) = 20 Expand the bracket

3(x + 2) is 3 lots of x + 2

x2x2x2

How many x bars? 3   How many 2s? 3

Put the bars in one row

xxx222

3(x + 2) = 3x + 6

This is expanding the bracket.

3(x + 2) = 21

xxx22221

Take off the 6: 3x = 15

x = 5

The quick way: expand the bracket, then solve.

Solve

2(x+3)=14
Expand2x + 6 = 14− 6 both sides2x = 8÷ 2 both sidesx = 4
Answerx = 4

Solve

4(x+2)=28
Expand4x + 8 = 28− 8 both sides4x = 20÷ 4 both sidesx = 5
Answerx = 5

Solve

2(x+3)=14
Expand2x + 6 = 14− 6 both sides2x = 8÷ 2 both sidesx = 4
Answerx = 4

Solve

3(x−1)=18
Expand3x − 3 = 18+ 3 both sides3x = 21÷ 3 both sidesx = 7
Answerx = 7

Solve

2(x+3)=14
Expand2x + 6 = 14− 6 both sides2x = 8÷ 2 both sidesx = 4
Answerx = 4

Solve

5(x+4)=35
Expand5x + 20 = 35− 20 both sides5x = 15÷ 5 both sidesx = 3
Answerx = 3

Solve

2(x+3)=14
Expand2x + 6 = 14− 6 both sides2x = 8÷ 2 both sidesx = 4
Answerx = 4

Solve

6(x−3)=42
Expand6x − 18 = 42+ 18 both sides6x = 60÷ 6 both sidesx = 10
Answerx = 10

Solve

2(x+3)=14
Expand2x + 6 = 14− 6 both sides2x = 8÷ 2 both sidesx = 4
Answerx = 4

Solve

2(x+9)=10
Expand2x + 18 = 10− 18 both sides2x = −8÷ 2 both sidesx = −4
Answerx = −4

Equations with brackets worksheet, page 1

Answer sheet

  1. I think of a number, add 4, then multiply by 3. The answer is 27. What was my number?

    5

  2. Solve 4(x + 1) = 2(x + 7)

    x = 5

  1. Solve 4(x + 3) = 32

    x = 5

  2. Solve 3(2x − 5) = 21

    x = 6

  3. Noor solves 2(x + 7) = 26 and gets x = 9.5. Find the right answer.

    x = 6
Exit tickets to print