Question

solve the inequality. graph the solution.
-2 ≤ 4 - 3a ≤ 13
solution:

Explanation:

Step1: Subtract 4 from all parts

Subtract 4 from $-2$, $4 - 3a$, and 13.
$-2-4\leq4 - 3a-4\leq13 - 4$
$-6\leq - 3a\leq9$

Step2: Divide all parts by -3

When dividing an inequality by a negative number, the inequality signs flip.
$\frac{-6}{-3}\geq\frac{-3a}{-3}\geq\frac{9}{-3}$
$2\geq a\geq - 3$
Which can be written as $-3\leq a\leq2$

Answer:

The solution is $-3\leq a\leq2$. On the number - line, there are closed - circles at $a=-3$ and $a = 2$, and the line is shaded between them.