Question

solve and graph the solution sets to the follow

1. |x + 2| ≤ 3

Explanation:

Step1: Remove absolute value

$$-3\leq x + 2\leq3$$

Step2: Subtract 2 from all parts

$$-3-2\leq x+2 - 2\leq3 - 2$$
$$-5\leq x\leq1$$

Answer:

The solution set is $x\in[-5,1]$. To graph it, draw a number line, mark points $-5$ and $1$ with closed circles (since the inequality includes equality), and shade the region between them.