Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 48

Solve the inequality $|-2x - 4| < 5$, and graph the solution set.

The expression $-2x - 4$ must represent a number that is less than or equal $5$ units from on either side of the number line. That is, $-2x - 4$ between $-5$ and $5$ (inclusive). So we have


$
\begin{equation}
\begin{aligned}

-5 < & -2x - 4 < 5
&&
\\
-1 < & -2x < 9
&& \text{Add each side by } 4
\\
\frac{1}{2} > & x > - \frac{9}{2}
&& \text{Divide each side by $-2$. Change signs $$}

\end{aligned}
\end{equation}
$



The solution set is $\displaystyle \left( - \frac{9}{2}, \frac{1}{2} \right)$.