SOLVING EQUATIONS
CONTAINING ABSOLUTE VALUE(S)
Note:
 if and only if
 if and only if
a + b = 3 or a + b =  3
 if any only if
a + b = + (x + y)
or a + b =  (x + y)
Solve for x in the following equation.
Example 3:
Either or
Step 1: Solve the equation
Step 2: Solve the equation
The answers are and .
Step 3:
Check the solution x = 0.3 by substituting 0.3 in the
original equation for x. If the left side of the equation equals the right
side of the equation after the substitution, you have found the correct
answer.

Left Side:

Right Side:
Since the left side of the original equation after we substituted the value 
0.3 for, the solution x = 0.3 is valid.
Check the solution x = by substituting in
the original equation for x. If the left side of the equation equals the
right side of the equation after the substitution, you have found the
correct answer.

Left Side:
 Right Side:
Since the left side of the original equation after we substituted the value
for, the solution is valid.
You can also check your answer by graphing (the left side of the original equation minus the right side
of the original equation). You will note that the two xintercepts on the
graph are located at x = 0.3 and
If you would like to review another example, click on Example
If you would like to test yourself by working some
problems similar to this example, click on Problem.
If you would like to go back to the equation table of contents, click
on Contents.
[Algebra]
[Trigonometry]
[Geometry]
[Differential Equations]
[Calculus]
[Complex Variables]
[Matrix Algebra]
S.O.S MATHematics home page
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.
Author:Nancy Marcus
Copyright © 19992017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC.  P.O. Box 12395  El Paso TX 79913  USA
users online during the last hour