Intermediate Algebra, Chapter 2, Test, Section Test, Problem 16

Evaluate the inequality $\displaystyle -6 \leq \frac{4}{3}x - 2 \leq 2$. Give the solution set in both interval and graph forms



$
\begin{equation}
\begin{aligned}
-6 + 2 &\leq \frac{4}{3} x - 2 + 2 \leq 2 + 2
&& \text{Add 2 on each side}\\
\\
-4 &\leq \frac{4}{3} x \leq 4
&& \text{Evaluate}\\
\\
-4 \left( \frac{3}{4} \right) &\leq x \leq 4 \left( \frac{3}{4} \right)
&& \text{Multiply each side by the reciprocal $\displaystyle \frac{4}{3}$ to solve for } x\\
\\
-3 &\leq x \leq 3
\end{aligned}
\end{equation}
$

This shows that the solution is the set of all real numbers in between and including $-3$ to $3$. Thus, the solution set in
interval form is $[-3, 3]$