The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Two Step Equations

Date: 02/24/98 at 01:14:38
From: Tyler Raymond
Subject: Two-step equations

I do not understand how to figure out two-step equations.  I think 
that I find a way and then find out that it does not apply to all 
cases.  Here are examples of my problems to help you help me solve my 

    7x - 2 = 12
    8x + 3 = 19

                  Thanks for the help,
                          Tyler Raymond

Date: 02/24/98 at 16:51:28
From: Doctor Rob
Subject: Re: Two-step equations

The aim is to isolate x on one side of the equation, so it looks like

    x = ...

    (or ... = x).

  Step 1:  Identify the term not involving x on the same side of the
           equation as the x. It may be positive or negative.

  Step 2:  Add its opposite (or negative) to both sides of the  
           equation. (Alternately, subtract it from both sides of the 

  Step 3:  Simplify. (Notice that the "x" term is on one side of the 
           equation, and a constant is on the other side.)

  Step 4:  Identify the coefficient of x in the term involving x. It  
           may be positive or negative.

  Step 5:  Divide both sides of the equation by that coefficient.

  Step 6:  Simplify.

You're done!  Your equation will now have the form "x = ...", which 
is what you were trying to get.

Example:  Solve  4*x + 7 = -13  for x.
Step 1:  That term is "+7".
Step 2:  Add -7 to both sides:  4*x + 7 - 7 = -13 - 7.
Step 3:  4*x = -20.
Step 4:  That coefficient is 4.
Step 5:  4*x/4 = -20/4.
Step 6:  x = -5.

Now try your two problems.

-Doctor Rob, The Math Forum   
Associated Topics:
Middle School Algebra
Middle School Equations

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.