#### 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

** Step 1: Isolate the absolute value expression.
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** Step2: Set the quantity inside the absolute value notation
equal to + and - the quantity on the other side of the equation.
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** Step 3:Solve for the unknown in both equations.
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** Step 4:Check your answer analytically or graphically.
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**Solve for x in the following equation.**

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Example 1:

Step 1:The absolute value is already isolated.

Either 2*x*-1=+5 or 2*x*-1=-5

Step 2:Solve the equation 2*x*-1=+5

Solve the equation 2*x*-1=-5

The answers are 3 and -2. These answers may not be solutions to the
equation.

Check the solution *x*=3 by substituting 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:

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:

The solutions are *x*=3 and -2.

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 3 and -2. This verifies our solutions graphically.

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

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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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