# Solving Two-Step Equations

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In these lessons, we will look at solving equations that require two steps.

The following figure shows how to solve two-step equations. Scroll down the page for more examples and solutions.

In order to solve two-step equations, we need to work backwards with regards to the order of operations. We would perform the addition & subtraction before multiplication & division.
1. Add or subtract to isolate the variable term.
2. Multiply or divide to solve for the variable.

Example:

In the equation 3x – 2 = 16, notice that the variable is being multiplied and has a term being subtracted. To isolate the variable, we need to add 2 to both sides and then divide both sides by 3.

Solve 3x – 2 = 16

Solution:

3x – 2 = 16
3x – 2 + 2 = 16 + 2 (add 2 to both sides)
3x = 18 (simplify)
x = 6 (divide both sides by 3)

Check:

3x – 2 = 16
3 • 6 – 2 = 16 (Substitute x = 6 into the original equation)

Example:

Consider the equation, . To isolate the variable, we need to subtract 2 from both sides and then multiply both sides by 4.

Solve

Solution:

Check:

How to solve basic two step equations?
Examples:
a) 2x + 3 = 9
b) 5x – 8 = 22
c) 9 – 2x = 23
d) –11 = 4x – 43
e) –15 = 5 – 5x How to solve two step linear equations with fractions?
In this video, the equations are solve by working with the fraction, not be clearing the fractions from the equation.
Examples:
1. 2x + 1/4 = 3/5
2. 2/5 x - 1/2 = 3/5
3. 1/4 = 3/5 x - 5
4. 2 1/5 = 2/3 - 1/2 x How to solve two step linear equations involving decimals?
Examples:
1) 0.3x - 2.16 = 9.9
2) x/2.1 + 4.93 = 10.45 How to solve the different types of two step equations?
Examples:
1) 2x + 3 = 25
2) x/4 - 2 = -5
3) 4 - 2x = 10
4) 4 = 6 - x/3
5) 4.3 = 1.5x - 5
6) x/3 - 3/4 = 1/6

Examples of solving two-step equations
1) b/3 + 13 = 11
2) 9g + 11 = 2
3) t/4 - 10 = -6
4) -a + 6 = 8
5) 15x + 3 = 48 How to solve a two-step equation? (undo PEMDAS in reverse to solve) Example:
4x + 8 = 24

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