Math Help for Section 3.7, Page 152

Solving
Equations Involving Absolute Value
Consider the absolute
value equation

    $|x|=3$.

The only solutions of this equation are $x=-3$ and $x=3$,
because these are the
only two real numbers whose distance from zero is 3. (See figure
below.)
In other
words, the absolute value equation $|x|=3$ has exactly two solutions:
$x=-3$ and $x=3$.

Study
Tip
As with a linear equation, you should check your solution(s) after
solving an absolute value equation. To check whether a given value is a
solution of an absolute value equation, substitute the value into the
original equation. If the substitution results in a true statement,
then the value is a solution of the equation. If the substitution
results in a false statement, then the value is not a solution of the
equation.