Equations with brackets

The Maths Habit

1Expand 3(x + 5)
3x + 15
2Expand 2(x − 4)
2x − 8
3Solve 4x + 3 = 23
x = 5

Sam tips all three bags out into one row. Which row does Sam get?

BagsRow ARow B

Row B. Every bag has a short bar, so there are three short bars.

x2x2x2xxx222
Expand
Multiply out the bracket, so there is no bracket left.
xx=
Equation
Two things that are equal, with an equals sign between them.
x=?
Solve
Find the value of the unknown.

Solve3(x+2)=18

x2x2x2
3 lots of x + 2
1Expand the bracket
Expand3x + 6 = 18
xxx22218
put the bars in one row
2Get the x's on their own
− 6 both sides3x = 12
xxx12
take the 2s off: 18 − 6 = 12
3Find one x
÷ 3 both sidesx = 4
x4
share 12 into 3

Which is the first line?

4(x + 5) = 32
4x + 5 = 324x + 20 = 32
4x + 20 = 32

Solve2(x+4)=14

xx4414
1Expand the bracket
Expand2x + 8 = 14
2Get the x's on their own
− 8 both sides2x = 6
3Find one x
÷ 2 both sidesx = 3
Answerx = 3

Solve3(x+1)=15

xxx11115
1Expand the bracket
Expand3x + 3 = 15
2Get the x's on their own
− 3 both sides3x = 12
3Find one x
÷ 3 both sidesx = 4
Answerx = 4

Solve2(x+4)=14

xx4414
1Expand the bracket
Expand2x + 8 = 14
2Get the x's on their own
− 8 both sides2x = 6
3Find one x
÷ 2 both sidesx = 3
Answerx = 3

Solve5(x+2)=40

xxxxx2222240
1Expand the bracket
Expand5x + 10 = 40
2Get the x's on their own
− 10 both sides5x = 30
3Find one x
÷ 5 both sidesx = 6
Answerx = 6
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Solve2(x+4)=14

xx4414
1Expand the bracket
Expand2x + 8 = 14
2Get the x's on their own
− 8 both sides2x = 6
3Find one x
÷ 2 both sidesx = 3
Answerx = 3

Solve4(x+1)=36

xxxx111136
1Expand the bracket
Expand4x + 4 = 36
2Get the x's on their own
− 4 both sides4x = 32
3Find one x
÷ 4 both sidesx = 8
Answerx = 8
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Solve2(x+4)=14

xx4414
1Expand the bracket
Expand2x + 8 = 14
2Get the x's on their own
− 8 both sides2x = 6
3Find one x
÷ 2 both sidesx = 3
Answerx = 3

Solve3(x+6)=27

xxx66627
1Expand the bracket
Expand3x + 18 = 27
2Get the x's on their own
− 18 both sides3x = 9
3Find one x
÷ 3 both sidesx = 3
Answerx = 3
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Solve2(x+5)=24

xx5524
1
Expand2x + 10 = 24
2
− 10 both sides2x = 14
3
÷ 2 both sidesx = 7
Answerx = 7

Solve5(x+1)=45

xxxxx1111145
1
Expand5x + 5 = 45
2
− 5 both sides5x = 40
3
÷ 5 both sidesx = 8
Answerx = 8

Solve3(x+4)=30

xxx44430
1
Expand3x + 12 = 30
2
− 12 both sides3x = 18
3
÷ 3 both sidesx = 6
Answerx = 6
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

xxxx−3−3−3−3?
  • A dashed bar takes away.
  • 4(x − 3) is 4 lots of x − 3.
  • Expand: 4x − 12
  • To undo − 12, + 12 both sides

Which is the first line?

3(x − 5) = 6
3x − 5 = 63x − 15 = 6
3x − 15 = 6

Solve4(x−1)=20

xxxx−1−1−1−120
1Expand the bracket
Expand4x − 4 = 20
2Get the x's on their own
+ 4 both sides4x = 24
3Find one x
÷ 4 both sidesx = 6
Answerx = 6

Solve2(x−3)=8

xx−3−38
1Expand the bracket
Expand2x − 6 = 8
2Get the x's on their own
+ 6 both sides2x = 14
3Find one x
÷ 2 both sidesx = 7
Answerx = 7

Solve4(x−1)=20

xxxx−1−1−1−120
1Expand the bracket
Expand4x − 4 = 20
2Get the x's on their own
+ 4 both sides4x = 24
3Find one x
÷ 4 both sidesx = 6
Answerx = 6

Solve3(x−2)=18

xxx−2−2−218
1Expand the bracket
Expand3x − 6 = 18
2Get the x's on their own
+ 6 both sides3x = 24
3Find one x
÷ 3 both sidesx = 8
Answerx = 8
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Solve4(x−1)=20

xxxx−1−1−1−120
1Expand the bracket
Expand4x − 4 = 20
2Get the x's on their own
+ 4 both sides4x = 24
3Find one x
÷ 4 both sidesx = 6
Answerx = 6

Solve5(x−1)=30

xxxxx−1−1−1−1−130
1Expand the bracket
Expand5x − 5 = 30
2Get the x's on their own
+ 5 both sides5x = 35
3Find one x
÷ 5 both sidesx = 7
Answerx = 7
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Solve4(x−1)=20

xxxx−1−1−1−120
1Expand the bracket
Expand4x − 4 = 20
2Get the x's on their own
+ 4 both sides4x = 24
3Find one x
÷ 4 both sidesx = 6
Answerx = 6

Solve2(x−5)=6

xx−5−56
1Expand the bracket
Expand2x − 10 = 6
2Get the x's on their own
+ 10 both sides2x = 16
3Find one x
÷ 2 both sidesx = 8
Answerx = 8
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Solve4(x−2)=12

xxxx−2−2−2−212
1
Expand4x − 8 = 12
2
+ 8 both sides4x = 20
3
÷ 4 both sidesx = 5
Answerx = 5

Solve3(x−4)=15

xxx−4−4−415
1
Expand3x − 12 = 15
2
+ 12 both sides3x = 27
3
÷ 3 both sidesx = 9
Answerx = 9

Solve5(x−3)=20

xxxxx−3−3−3−3−320
1
Expand5x − 15 = 20
2
+ 15 both sides5x = 35
3
÷ 5 both sidesx = 7
Answerx = 7
Remember1Expand the bracket2Get the x's on their own+ or − both sides3Find one x÷ both sides

Equations with brackets worksheet, page 1

Equations with brackets worksheet, page 2

Answer sheet

Is the first line right? Thumbs up: yes. Thumbs down: no.

  1. 2(x + 6) = 30   first line 2x + 12 = 30

    Yes

  2. 4(x + 3) = 28   first line 4x + 3 = 28

    No: 4x + 12 = 28

  3. 5(x − 4) = 15   first line 5x − 20 = 15

    Yes

  4. 3(x − 2) = 21   first line 3x − 2 = 21

    No: 3x − 6 = 21

  5. 10(x + 1) = 60   first line 10x + 10 = 60

    Yes

  1. x = 4 is the answer to 3(x + □) = 27. What number goes in the box?

    5

  2. Solve 2(3x + 2) = 34

    x = 5

  3. Write your own equation with a bracket. Make the answer x = 3.

    For example 2(x + 1) = 8

  1. Solve 3(x + 5) = 21xxx55521Step 1 is given: expand, so 3x + 15 = 21.

    Answer x = 2

  2. Solve 4(x − 2) = 20xxxx−2−2−2−220

    Answer x = 7

  3. Solve 5(x + 3) = 40. Show your steps.

    Answer x = 5
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