Question

solve for $u$ and graph the solution.
$3 \leq |u + 6|$
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 \(|u + 6|\geq3\), we use the property \(|x|\geq a\) implies \(x\geq a\) or \(x\leq - a\).
So \(u+6\geq3\) or \(u + 6\leq-3\).

Step2: Solve \(u+6\geq3\)

Subtract 6 from both sides: \(u+6 - 6\geq3 - 6\), which gives \(u\geq - 3\).

Step3: Solve \(u + 6\leq-3\)

Subtract 6 from both sides: \(u+6-6\leq-3 - 6\), which gives \(u\leq-9\).

Answer:

The solution of the inequality \(3\leq|u + 6|\) is \(u\leq-9\) or \(u\geq - 3\).
To graph:

• For \(u\leq-9\): Click on \(-9\) (filled - in circle) and an arrowhead to the left.
• For \(u\geq - 3\): Click on \(-3\) (filled - in circle) and an arrowhead to the right.