Question

solve for p and graph the solution. |p - 1| ≥ 4 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: Recall absolute - value inequality rule

For \(|x|\geq a\) (\(a\geq0\)), it is equivalent to \(x\geq a\) or \(x\leq - a\). Here \(x = p - 1\) and \(a = 4\), so \(p-1\geq4\) or \(p - 1\leq-4\).

Step2: Solve \(p-1\geq4\)

Add 1 to both sides: \(p-1 + 1\geq4 + 1\), so \(p\geq5\).

Step3: Solve \(p - 1\leq-4\)

Add 1 to both sides: \(p-1+1\leq - 4 + 1\), so \(p\leq-3\).

Answer:

The solution set is \(p\leq - 3\) or \(p\geq5\). On the number - line, we have a ray starting at \(p=-3\) with a closed circle (since the inequality is \(\leq\)) and going to the left, and a ray starting at \(p = 5\) with a closed circle (since the inequality is \(\geq\)) and going to the right.