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SOLVING EQUATIONS
CONTAINING ABSOLUTE VALUE(S)

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Note:
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** if and only if
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** 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 2:

Either or

Step 1: Solve

Step 2:
Solve 5 *x* + 7 = - (2*x*
+ 11) :

The answers are and .

Step 4: Check the solution 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 equals the right side of the
original equation when is substituted for, then is a valid solution.

Check the solution 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
equals the right side of the original equation when is
substituted for, then is a valid solution.

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

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**### 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.

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If you would like to go back to the equation table of contents, click
on Contents**.

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[Algebra]
[Trigonometry]
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[Geometry]
[Differential Equations]
[Calculus]
[Complex Variables]
[Matrix Algebra]

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**Author:Nancy Marcus**

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