College Algebra, Chapter 1, 1.7, Section 1.7, Problem 34

Solve the inequality $|5x -2| < 6 $. Express the answer using interval notation.

We have,


$
\begin{equation}
\begin{aligned}
5x -2 &< 6 && \text{and}& -(5x -2) &< 6 && \text{Divide both sides by -1}\\
\\
5x-2 &< 6 && \text{and}& 5x-2 &> -6 && \text{Add 2}\\
\\
5x &< 8 && \text{and}& 5x &> -4 && \text{Divide by 5}\\
\\
x &< \frac{8}{5} && \text{and}& x &> -\frac{4}{5}
\end{aligned}
\end{equation}
$


The solution set is $\displaystyle \left( -\frac{4}{5}, \frac{8}{5} \right)$