Question

solve for w and graph the solution.
4 ≤ |w + 2|
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: Solve the absolute - value inequality

For \(|x|\geq a\) (\(a = 4\), \(x=w + 2\)), the solution is \(x\leq - a\) or \(x\geq a\).
So \(w + 2\leq-4\) or \(w + 2\geq4\).

Step2: Solve \(w + 2\leq-4\)

Subtract 2 from both sides: \(w+2-2\leq - 4-2\), \(w\leq - 6\).

Step3: Solve \(w + 2\geq4\)

Subtract 2 from both sides: \(w+2 - 2\geq4 - 2\), \(w\geq2\).

Answer:

The solution of the inequality \(4\leq|w + 2|\) is \(w\leq - 6\) or \(w\geq2\).
To graph: For \(w\leq - 6\), click on \(-6\) (filled - in circle) and an arrowhead to the left. For \(w\geq2\), click on \(2\) (filled - in circle) and an arrowhead to the right.