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