Solving Equations with Variables on Both Sides

Variables on Both Sides

100

5x + 6 = 2x + 15

x = 3

200

7x - 4 = 20 + 3x

x = 6

300

-7x - 2 = 24 - 9x

x = 13

400

-x - 29 = 13 + 2x

-14 = x

500

27 - x - 10x = x - 33

x = 5

Multi-Step with Distributive Property 1

100

4(5n-7) = 10n + 2

n = 3

200

9(x + 3) = 4x - 3

x = -6

300

2(12 - 8x) = x - 11x

x = 4

400

3t + 8(2t - 6) = 2 + 14t

t= 10

500

2v + 18 = 16 - 4(v+7)

v=-5

Multi-Step with Distributive Property 2

100

4x - (9 -3x) = 8x - 1

x = -8

200

12(3 + y) = 5(2y + 8)

y=2

300

-7(1-4m) = 13(2m - 3)

m = -16

400

9(11-k) = 3(3k-9)

k = 7

500

4x + 5(7x - 3) = 9(x-5)

x = -1

You've Got This!

100

-(2n - 8) = -2 - (n+4)

14= n

200

2(5c + 2) - 2c = 3(2c + 3) + 7

c = 6

300

2(6d + 3) = 18 - 3(16-3d)

d = -12

400

8(4u-1)-12u = 11(2u-6)

u = 29

500

-5 - (15y-1) = 2(7y-16)-y

y = 1.5

Special Cases

100

-2(x+1) = -2x + 5

No solution

200

2x + 2x + 2 = 4x + 2

Identity. Infinitely Many Solutions

300

7x - 9 - 3x = 4(x + 3) + 1

No solution.

400

3(5x + 2) = 15x

No Solution.

500

-2(4y + 1) = -8y - 2

Identity. Infinitely many solutions.