Question

solve the compound inequality.
$-9\leq 3x - 3 < 3$
graph the solution on the number line.

Explanation:

Step1: Add 3 to all parts

$-9 + 3 \leq 3x - 3 + 3 < 3 + 3$
$\implies -6 \leq 3x < 6$

Step2: Divide all parts by 3

$\frac{-6}{3} \leq \frac{3x}{3} < \frac{6}{3}$
$\implies -2 \leq x < 2$

Step3: Graph the solution

• On the number line, plot a closed dot at $x=-2$ (since the inequality includes equality) and an open dot at $x=2$ (since the inequality does not include equality).
• Shade the region between $-2$ and $2$.

Answer:

The solution to the compound inequality is $\boldsymbol{-2 \leq x < 2}$.
For the graph:

• Place a closed dot at $-2$, an open dot at $2$, and shade the segment connecting these two points on the provided number line.