Question

solve for q and graph the solution. |q - 3| ≥ 3. click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or click on them. solve absolute value inequalities (90). not feeling ready yet? these can help: work it out. graph inequalities.

Explanation:

Step1: Recall absolute - value inequality rule

For \(|x|\geq a\) (\(a\geq0\)), it is equivalent to \(x\geq a\) or \(x\leq - a\). Here \(x = q - 3\) and \(a = 3\), so we have \(q-3\geq3\) or \(q - 3\leq-3\).

Step2: Solve \(q-3\geq3\)

Add 3 to both sides of the inequality \(q-3\geq3\). We get \(q-3 + 3\geq3 + 3\), which simplifies to \(q\geq6\).

Step3: Solve \(q - 3\leq-3\)

Add 3 to both sides of the inequality \(q - 3\leq-3\). We get \(q-3+3\leq-3 + 3\), which simplifies to \(q\leq0\).

Answer:

The solution of the inequality \(|q - 3|\geq3\) is \(q\leq0\) or \(q\geq6\). On the number - line, we mark a closed circle at \(q = 0\) and draw an arrow to the left, and mark a closed circle at \(q = 6\) and draw an arrow to the right.