Question

solve for w and graph the solution. |w + 125| ≥ 25 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: Split absolute - value inequality

For \(|w + 125|\geq25\), we have two cases: \(w + 125\geq25\) and \(w+125\leq - 25\).

Step2: Solve \(w + 125\geq25\)

Subtract 125 from both sides: \(w\geq25 - 125\), so \(w\geq - 100\).

Step3: Solve \(w + 125\leq - 25\)

Subtract 125 from both sides: \(w\leq-25 - 125\), so \(w\leq - 150\).

Answer:

The solution is \(w\leq - 150\) or \(w\geq - 100\). On the number - line, we mark a closed circle at \(w=-150\) and draw an arrow to the left, and mark a closed circle at \(w = - 100\) and draw an arrow to the right.