Introduction

Two step equations generally consist of exactly three terms, a variable term and number on one side as well as a number on the other side.

The phrase “multi-step equation” simply means an equation that has a few more “bells and whistles” than a two-step equation.  Multi-step equations may have several variable terms or number terms that need to be combined before the equation can be solved. 

3a + 5 + 4a + 7 = 11 + 22                            6b + 12 + 8b  = 40

Notice that by combining like terms, each of the above equations can be changed into a two-step equation.

The first equation can be simplified like this:

   3a + 5 + 4a + 7 = 11 + 22

                7a + 12 = 33

The second equation can be simplified like this:

   6b + 12 + 8b  = 40

           14b + 12 = 40

Lesson

In order to be able to solve multi-step equations, it is important to understand the concept of like terms.  

Consider the following terms:   y, 4x, 9, 15, 6x, 2y, 7x, 10, 4y, -8

These terms can be split into three categories: 

When adding and subtracting numbers, only like terms can be combined. 

The following equation can be simplified by combining like terms.

     3x + 8 + 2x = 11 + 27

Before solving, combine like terms on each side.

     On the left side, 3x + 2x = 5x.

     On the right side, 11 + 27 = 38.

It often helps to underline like terms in order to differentiate them.  You may even find it helpful to use colored pencils to differentiate variable terms from number terms.  The variable terms in the example can be colored red and the number terms blue.

When two terms are multiplied by a single number, the distributive property can be used in your solution.

Example:

     4(x + 6) – 11 = 25

Solution:

Try It

Solve the following equations:

1)  5b + 8 + 3b + 4 = 40 – 4                               

Solution:

2)  5(x + 2) + 11 = 36

Solution: