Question

solve for a and graph the solution. |a + 5| ≤ 3 click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| \leq c\) (where \(c\geq0\)), the solution is \(-c \leq x \leq c\). Here, \(x = a + 5\) and \(c = 3\), so we get \(-3 \leq a + 5 \leq 3\).

Step2: Solve left inequality

Subtract 5 from all parts: \(-3 - 5 \leq a + 5 - 5 \leq 3 - 5\).
Simplify: \(-8 \leq a \leq -2\).
To graph, on the number line, we have filled - in circles at \(-8\) and \(-2\) (since the inequality is "less than or equal to") and a line segment connecting them.

Answer:

\(-8 \leq a \leq -2\)