Question

solve for p and graph the solution.
|-6p - 60| ≤ 30
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: Apply the absolute - value inequality rule

If \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\). For \(|- 6p - 60|\leq30\), we have \(-30\leq - 6p - 60\leq30\).

Step2: Solve the left - hand side of the compound inequality

Add \(60\) to all parts of the compound inequality: \(-30 + 60\leq-6p-60 + 60\leq30 + 60\), which simplifies to \(30\leq - 6p\leq90\).

Step3: Divide by \(-6\) and reverse the inequality signs

When dividing by a negative number (\(-6\)), the inequality signs reverse. So \(\frac{30}{-6}\geq p\geq\frac{90}{-6}\), which gives \(-15\leq p\leq - 5\).

Answer:

The solution for \(p\) is \(-15\leq p\leq - 5\). On the number line, we graph a line segment with endpoints at \(p=-15\) and \(p = - 5\) (both endpoints are filled - in circles since the inequality is \(\leq\)).