Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

​How to Solve

​To solve equations with variables on both sides:

​

1. collect the all variable terms on one side and the constant terms on the other side.

2. ​Isolate the variable.

​Solve

​15 - 2x = -7x

​Solve

​-3x = 2x + 19

​Solve

​6(4 - z) = 2z

Multiple Choice

Solve.

9 - m = 2m

• 3

• 6

• -7

• 7

Multiple Choice

Solve.

4k - 1 = 7k + 2

• 11

• -1

• 5

• -6

Multiple Choice

2(n - 2) = 5n + 5

• -4

• 2

• 10

• -3

​Solve

​3 - 4x = -7 - 4x

​Solving Equations with No Solution

​Some equations do not have one solution. Equations can also have no solution or infinitely many solutions.

​

When solving an equation that has no solution, you will obtain an equivalent equation that is not true for any value of the variable, such as 0 = 2.

​

​4 - x = 8 - x

​Solve

​8h - 4 = 4(2h - 1)

​Solving Equations with Infinite Solutions

​When solving an equation that has infinitely many solutions, you will obtain an equivalent equation that is true for all values of the variable, such as − 5 = − 5.

​

​8f = 2f + 6f

Multiple Choice

How many solutions does this equation have?

8k - 4 = 8k - 4

• Infinite

• None

• One

• Two

Multiple Choice

How many solutions does this equation have?

3x = 3x - 8

• Infinite

• None

• One

• Two