Question

solve for q and graph the solution. 5 ≤ |q + 25| click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or click on them. to change endpoints from filled - in circles to empty circles, 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 \(|x|\geq a\) (\(a\geq0\)), the solution is \(x\geq a\) or \(x\leq - a\). Given \(5\leq|q + 25|\), we have \(q+25\geq5\) or \(q + 25\leq-5\).

Step2: Solve \(q+25\geq5\)

Subtract 25 from both sides: \(q+25 - 25\geq5 - 25\), so \(q\geq - 20\).

Step3: Solve \(q + 25\leq-5\)

Subtract 25 from both sides: \(q+25-25\leq - 5-25\), so \(q\leq - 30\).

Answer:

The solution set is \(q\leq - 30\) or \(q\geq - 20\). On the number - line, we mark a closed circle at \(q=-30\) and draw an arrow to the left, and mark a closed circle at \(q = - 20\) and draw an arrow to the right.