Question

solve the compound inequality. -6 ≤ 4x + 6 ≤ 26 graph the solution on the number line.

Explanation:

Step1: Subtract 6 from all parts

\[

$$\begin{align*} -6-6&\leq4x + 6-6\leq26 - 6\\ -12&\leq4x\leq20 \end{align*}$$

\]

Step2: Divide all parts by 4

\[

$$\begin{align*} \frac{-12}{4}&\leq\frac{4x}{4}\leq\frac{20}{4}\\ - 3&\leq x\leq5 \end{align*}$$

\]

Answer:

The solution is $-3\leq x\leq5$. On the number - line, you would use a closed circle at $x = - 3$ and $x = 5$ and shade the region between them.