#### SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

**
Note:
**

**
**

** if and only if
**

** if and only if ***a*+*b*=3 or *a*+*b*=-3

** Step 1:Isolate the absolute value expression.
**

** Step2:Set the quantity inside the absolute value notation
equal to + and - the quantity on the other side of the equation.
**

** Step 3:Solve for the unknown in both equations.
**

** Step 4:Check your answer analytically or graphically.
**

**
**

**Solve for x in the following equation.**

Example 2:

Step 1:The absolute value is already isolated.

**
**

Since and , 5*x*+7=3 or 5*x*+7=-3

Step 2:Set the quantity within the absolute value notation to

Step 3:Solve for x in the equation 5*x*+7=3

Solve for x in the equation 5*x*+7=-3.

The answers are and -2.

Step 4: Check the solutions because answers are not always valid
solutions to the equation.

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

Check the solution x = -2 by substituting -2 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 -2 for, the solution *x*=-2 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 x-intercepts on the graph are located
at and -2. this verifies our solutions graphically.

**If you would like to work another example, click on Example
**

**
****If you would like to test yourself by working some problems similar to this
example, click on Problems**

**
**

**
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 © 1999-2017 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