Equation Cheat Sheet

Five equation types · five difficulty levels · increasing complexity left to right.

Level 1
Easiest

Level 2

Level 3

Level 4

Level 5
Hardest

One-Step

ax = b
x + b = c

3x = 12

1.3x/3 = 12/3

x = 4

x + 7 = 15

1.x + 7 = 15 − 7

x = 8

5x = −30

1.5x/5 = −30/5

x = −6

x − 11 = 4

1.x ~~− 11~~ = 4 + 11

x = 15

−4x = 36

1.−4x/−4 = 36/−4

x = −9

Two-Step

ax + b = c

2x + 3 = 9

1.2x = 9 − 3 = 6

2.x = 6/2

x = 3

4x − 5 = 11

1.4x = 11 + 5 = 16

2.x = 16/4

x = 4

7x + 14 = 0

1.7x = −14

2.x = −14/7

x = −2

3x − 8 = 16

1.3x = 24

2.x = 24/3

x = 8

−5x + 20 = 45

1.−5x = 25

2.x = 25/−5

x = −5

Distribution

a(x + b) = c

2(x + 3) = 10

÷2x + 3 = 5

−3x = 2

x = 2

3(x − 4) = 15

÷3x − 4 = 5

+4x = 9

x = 9

5(x + 2) = 35

÷5x + 2 = 7

−2x = 5

x = 5

4(2x − 1) = 28

÷42x − 1 = 7

+12x = 8

÷2x = 4

x = 4

6(3x + 5) = 48

÷63x + 5 = 8

−53x = 3

÷3x = 1

x = 1

Both Sides

ax + b = cx + d

5x = 2x + 9

−2x3x = 9

÷3x = 3

x = 3

7x + 1 = 4x + 10

−4x3x + 1 = 10

−13x = 9

÷3x = 3

x = 3

8x − 3 = 5x + 9

−5x3x − 3 = 9

+33x = 12

÷3x = 4

x = 4

10x + 6 = 3x − 8

−3x7x + 6 = −8

−67x = −14

÷7x = −2

x = −2

12x − 15 = 7x + 20

−7x5x − 15 = 20

+155x = 35

÷5x = 7

x = 7

Proportion

a/b = c/x

1/2 = 3/x

×1·x = 2·3

=x = 6

x = 6

3/4 = 9/x

×3x = 36

÷3x = 12

x = 12

5/8 = 15/x

×5x = 120

÷5x = 24

x = 24

7/3 = x/12

×3x = 84

÷3x = 28

x = 28

11/6 = x/18

×6x = 198

÷6x = 33

x = 33

Strategy: always work left→right (easier→harder). Keep x on the left. Do inverse operations — undo addition with subtraction, undo multiplication with division.