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Absolute Value Equations
Equations with a variable or variables within absolute value bars are known as
Absolute
Value Equations
.
Examples:
⏐
x  3
⏐
=
5
⏐
2x  3
⏐
+ x =
2
Method To Solve Absolute Value Equations:
To solve absolute value equations, remember to do the following:
•
Isolate the absolute value expression on one side of =. So for example, use the
Addition Property of Equality
to subtract x from both sides of
⏐
2x  3
⏐
+ x =
2
to
result in
⏐
2x  3
⏐
=
2  x
.
•
Use the
Absolute Value Equation Property
to solve two cases without the absolute
values, one positive and one negative.
In the above example, you would solve
2x  3 =
2  x
and
2x  3 =
(2 – x).
•
After solving,
check all answers
.
You may get extraneous solutions!
In the example
above, we would get answers of x=5/3 and x=1.
It turns out that both work.
Example:
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 Fall '09
 Crandall
 Anthropology, Quadratic equation, Negative and nonnegative numbers, absolute value equation, Division Property of Equality

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