Question

solve for z and graph the solution. |z + 28| ≥ 2 click two endpoints to graph a line - segment, an endpoint and an arrow - head to graph a ray, or two arrow - heads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Solve the absolute - value inequality

For \(|z + 28|\geq2\), we consider two cases.
Case 1: \(z + 28\geq2\).
Subtract 28 from both sides: \(z+28 - 28\geq2 - 28\), so \(z\geq - 26\).
Case 2: \(z + 28\leq - 2\).
Subtract 28 from both sides: \(z+28 - 28\leq - 2-28\), so \(z\leq - 30\).

Answer:

The solution is \(z\leq - 30\) or \(z\geq - 26\). On the number - line, we mark a closed circle at \(z=-30\) and draw an arrow to the left, and mark a closed circle at \(z = - 26\) and draw an arrow to the right.