Solving two-step equations

The Maths Habit

1Solve x + 7 = 12
x712
x = 5
2Solve x − 4 = 9
x− 49
x = 13
3Solve 3x = 15
xxx15
x = 5

The scales balance. Sam takes the cubes off the left pan. What happens? How can Sam make the scales balance again?

The left pan goes up. Take the same number of cubes off the right pan too. Do the same to both sides.

xx
Equation
Two things that are equal, with an equals sign between them.
x
Unknown
A letter that stands for a number we do not know yet.
x=?
Solve
Find the value of the unknown.

Solve 2x + 3 = 11

xx311
the equation
1Get the x's on their own
− 3 both sides2x = 8
xx8
take 3 off both pans
2Find one x
÷ 2 both sidesx = 4
x4
share each pan into 2

Get the x's on their own. What do you do to both sides?

3x + 4 = 19xxx419 − 4 both sides

Which comes first?

2x + 8 = 18
÷ 2 both sides− 8 both sides
− 8 both sides first

Solve 2x + 5 = 17

xx517
1Get the x's on their own
− 5 both sides2x = 12
2Find one x
÷ 2 both sidesx = 6
Answerx = 6

Solve 3x + 2 = 14

xxx214
1Get the x's on their own
− 2 both sides3x = 12
2Find one x
÷ 3 both sidesx = 4
Answerx = 4

Solve 2x + 5 = 17

xx517
1Get the x's on their own
− 5 both sides2x = 12
2Find one x
÷ 2 both sidesx = 6
Answerx = 6

Solve 4x + 3 = 23

xxxx323
1Get the x's on their own
− 3 both sides4x = 20
2Find one x
÷ 4 both sidesx = 5
Answerx = 5
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solve 2x + 5 = 17

xx517
1Get the x's on their own
− 5 both sides2x = 12
2Find one x
÷ 2 both sidesx = 6
Answerx = 6

Solve 5x + 1 = 31

xxxxx131
1Get the x's on their own
− 1 both sides5x = 30
2Find one x
÷ 5 both sidesx = 6
Answerx = 6
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solve 2x + 5 = 17

xx517
1Get the x's on their own
− 5 both sides2x = 12
2Find one x
÷ 2 both sidesx = 6
Answerx = 6

Solve 10x + 6 = 46

xxxxxxxxxx646
1Get the x's on their own
− 6 both sides10x = 40
2Find one x
÷ 10 both sidesx = 4
Answerx = 4
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solve 3x + 5 = 20

xxx520
1Get the x's on their own
− 5 both sides3x = 15
2Find one x
÷ 3 both sidesx = 5
Answerx = 5

Solve 4x + 2 = 30

xxxx230
1Get the x's on their own
− 2 both sides4x = 28
2Find one x
÷ 4 both sidesx = 7
Answerx = 7

Solve 5x + 3 = 43

xxxxx343
1Get the x's on their own
− 3 both sides5x = 40
2Find one x
÷ 5 both sidesx = 8
Answerx = 8
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

xxxx− 3?
  • A dashed tile takes away.
  • 4x − 3 is four x's, take away 3.
  • To undo − 3, + 3 both sides

Get the x's on their own. What do you do to both sides?

5x − 2 = 18xxxxx− 218 + 2 both sides

Solve 3x − 2 = 13

xxx− 213
1Get the x's on their own
+ 2 both sides3x = 15
2Find one x
÷ 3 both sidesx = 5
Answerx = 5

Solve 2x − 3 = 11

xx− 311
1Get the x's on their own
+ 3 both sides2x = 14
2Find one x
÷ 2 both sidesx = 7
Answerx = 7

Solve 3x − 2 = 13

xxx− 213
1Get the x's on their own
+ 2 both sides3x = 15
2Find one x
÷ 3 both sidesx = 5
Answerx = 5

Solve 5x − 4 = 21

xxxxx− 421
1Get the x's on their own
+ 4 both sides5x = 25
2Find one x
÷ 5 both sidesx = 5
Answerx = 5
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solve 3x − 2 = 13

xxx− 213
1Get the x's on their own
+ 2 both sides3x = 15
2Find one x
÷ 3 both sidesx = 5
Answerx = 5

Solve 3x − 5 = 16

xxx− 516
1Get the x's on their own
+ 5 both sides3x = 21
2Find one x
÷ 3 both sidesx = 7
Answerx = 7
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solve 3x − 2 = 13

xxx− 213
1Get the x's on their own
+ 2 both sides3x = 15
2Find one x
÷ 3 both sidesx = 5
Answerx = 5

Solve 4x − 6 = 30

xxxx− 630
1Get the x's on their own
+ 6 both sides4x = 36
2Find one x
÷ 4 both sidesx = 9
Answerx = 9
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solve 2x − 7 = 9

xx− 79
1Get the x's on their own
+ 7 both sides2x = 16
2Find one x
÷ 2 both sidesx = 8
Answerx = 8

Solve 5x − 3 = 32

xxxxx− 332
1Get the x's on their own
+ 3 both sides5x = 35
2Find one x
÷ 5 both sidesx = 7
Answerx = 7

Solve 3x − 4 = 26

xxx− 426
1Get the x's on their own
+ 4 both sides3x = 30
2Find one x
÷ 3 both sidesx = 10
Answerx = 10
Remember1Get the x's on their own+ or − both sides2Find one x÷ both sides

Solving two-step equations worksheet, page 1

Solving two-step equations worksheet, page 2

Answer sheet

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

  1. 3x + 5 = 26   − 5 both sides

    Yes

  2. 4x − 7 = 13   − 7 both sides

    No: + 7 both sides

  3. 2x + 6 = 20   ÷ 2 both sides

    No: − 6 both sides

  4. 5x − 1 = 24   + 1 both sides

    Yes

  5. 10x + 3 = 53   − 3 both sides

    Yes

  1. x = 4 is the answer to 3x + □ = 20. What number goes in the box?

    8

  2. I think of a number. I multiply it by 7. Then I take away 4. I get 45. What is my number?

    7

  3. Write your own equation with the answer x = 3. Use two steps.

    For example 2x + 1 = 7

  1. Solve 4x + 3 = 27. Step 1 is given: − 3 both sides, so 4x = 24.

    Answer x = 6
    xxxx327

  2. Solve 2x − 5 = 13

    Answer x = 9
    xx− 513

  3. Solve 5x + 2 = 37. Show your steps.

    x = 7
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