Equations: the unknown on both sides

The Maths Habit

1Simplify 5x − 2x
3x
2Simplify 6x − 4x
2x
3Solve 2x + 3 = 13
x = 5

The scales balance. Sam takes two bags off each pan. Does it still balance?

Yes. The same came off both sides. Now one bag and two cubes balance five cubes.

xxxx
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.
xxxx
Both sides
The left and the right of the equals sign. Do the same to both sides.

Which side has fewer x's? What do you take off both sides?

5x + 1 = 3x + 9xxxxx1xxx9 − 3x both sides

Solve 4x + 2 = 3x + 9

xxxx2xxx9
1Take off the fewer x's
− 3x both sidesx + 2 = 9
2Get the x's on their own
− 2 both sidesx = 7
Answerx = 7

Solve 3x + 5 = 2x + 11

xxx5xx11
1Take off the fewer x's
− 2x both sidesx + 5 = 11
2Get the x's on their own
− 5 both sidesx = 6
Answerx = 6

Solve 4x + 2 = 3x + 9

xxxx2xxx9
1Take off the fewer x's
− 3x both sidesx + 2 = 9
2Get the x's on their own
− 2 both sidesx = 7
Answerx = 7

Solve 5x + 1 = 4x + 9

xxxxx1xxxx9
1Take off the fewer x's
− 4x both sidesx + 1 = 9
2Get the x's on their own
− 1 both sidesx = 8
Answerx = 8
Remember1Take off the fewer x's− x's both sides2Get the x's on their own− both sides

Solve 4x + 2 = 3x + 9

xxxx2xxx9
1Take off the fewer x's
− 3x both sidesx + 2 = 9
2Get the x's on their own
− 2 both sidesx = 7
Answerx = 7

Solve 2x + 3 = x + 7

xx3x7
1Take off the fewer x's
− x both sidesx + 3 = 7
2Get the x's on their own
− 3 both sidesx = 4
Answerx = 4
Remember1Take off the fewer x's− x's both sides2Get the x's on their own− both sides

Solve 4x + 2 = 3x + 9

xxxx2xxx9
1Take off the fewer x's
− 3x both sidesx + 2 = 9
2Get the x's on their own
− 2 both sidesx = 7
Answerx = 7

Solve 6x + 4 = 5x + 13

xxxxxx4xxxxx13
1Take off the fewer x's
− 5x both sidesx + 4 = 13
2Get the x's on their own
− 4 both sidesx = 9
Answerx = 9
Remember1Take off the fewer x's− x's both sides2Get the x's on their own− both sides

Which comes first?

6x + 3 = 3x + 18
− 3 both sides− 3x both sides
− 3x both sides first

Solve 5x + 3 = 3x + 13

xxxxx3xxx13
1Take off the fewer x's
− 3x both sides2x + 3 = 13
2Get the x's on their own
− 3 both sides2x = 10
3Find one x
÷ 2 both sidesx = 5
Answerx = 5

Solve 4x + 1 = 2x + 15

xxxx1xx15
1Take off the fewer x's
− 2x both sides2x + 1 = 15
2Get the x's on their own
− 1 both sides2x = 14
3Find one x
÷ 2 both sidesx = 7
Answerx = 7

Solve 5x + 3 = 3x + 13

xxxxx3xxx13
1Take off the fewer x's
− 3x both sides2x + 3 = 13
2Get the x's on their own
− 3 both sides2x = 10
3Find one x
÷ 2 both sidesx = 5
Answerx = 5

Solve 5x + 3 = 2x + 18

xxxxx3xx18
1Take off the fewer x's
− 2x both sides3x + 3 = 18
2Get the x's on their own
− 3 both sides3x = 15
3Find one x
÷ 3 both sidesx = 5
Answerx = 5
Remember1Take off the fewer x's− x's both sides2Get the x's on their own− both sides3Find one x÷ both sides

Solve 5x + 3 = 3x + 13

xxxxx3xxx13
1Take off the fewer x's
− 3x both sides2x + 3 = 13
2Get the x's on their own
− 3 both sides2x = 10
3Find one x
÷ 2 both sidesx = 5
Answerx = 5

Solve 6x + 2 = 4x + 14

xxxxxx2xxxx14
1Take off the fewer x's
− 4x both sides2x + 2 = 14
2Get the x's on their own
− 2 both sides2x = 12
3Find one x
÷ 2 both sidesx = 6
Answerx = 6
Remember1Take off the fewer x's− x's both sides2Get the x's on their own− both sides3Find one x÷ both sides

Solve 5x + 3 = 3x + 13

xxxxx3xxx13
1Take off the fewer x's
− 3x both sides2x + 3 = 13
2Get the x's on their own
− 3 both sides2x = 10
3Find one x
÷ 2 both sidesx = 5
Answerx = 5

Solve 4x + 5 = x + 17

xxxx5x17
1Take off the fewer x's
− x both sides3x + 5 = 17
2Get the x's on their own
− 5 both sides3x = 12
3Find one x
÷ 3 both sidesx = 4
Answerx = 4
Remember1Take off the fewer x's− x's both sides2Get the x's on their own− both sides3Find one x÷ both sides

Equations: the unknown on both sides worksheet, page 1

Equations: the unknown on both sides worksheet, page 2

Answer sheet

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

  1. 6x + 1 = 4x + 9   − 4x both sides

    Yes

  2. 5x + 4 = 2x + 19   − 5x both sides

    No: − 2x both sides

  3. 4x + 7 = 3x + 10   − 7 both sides

    No: − 3x both sides

  4. 3x + 2 = x + 12   − x both sides

    Yes

  5. 7x + 1 = 5x + 11   − 5x both sides

    Yes

  1. Solve 2x + 13 = 5x + 1. Which side has fewer x's?

    x = 4

  2. I think of a number. Four times my number add 9 is the same as my number add 30. What is my number?

    7

  3. Write your own equation with x on both sides. Make the answer x = 3.

    For example 3x + 1 = 2x + 4

  1. Solve 4x + 5 = 3x + 11. Step 1: − 3x both sides

    Answer x = 6
    xxxx5xxx11

  2. Solve 5x + 3 = 2x + 24

    Answer x = 7

  3. Solve 7x + 3 = 4x + 15. Show your steps.

    Answer x = 4
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