Log in Register

Login to your account

Username *
Password *
Remember Me

Create an account

Fields marked with an asterisk (*) are required.
Name *
Username *
Password *
Verify password *
Email *
Verify email *

Newsletter

Sign up for our newsletter!
Please wait

Multi-Step Equations

Introduction

Multi-step_equations_visuals_1

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: 

 

Multi-step_equations_visuals_6

 

  

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.

 

 Multi-step_equations_visuals_2 

 

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:

 

 

Multi-step_equations_visuals_3

Try It

Solve the following equations:

 

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

 

 

Solution:

Multi-step_equations_visuals_4 

 

 

 

2)  5(x + 2) + 11 = 36

 

 

Solution:

Multi-step_equations_visuals_5


 

 

Related Links:

Looking for a different lesson on solving equations?  Try the links below.

 

Related Lessons

Looking for something else?  Explore our menu of general math or algebra lessons.

Copyright © 2014. Free Math Resource.
All Rights Reserved.