Question

solve for z and graph the solution. 30 ≥ |z + 140| 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. -170 -160 -150 -140 -130 -120 -110 -100 -90

Explanation:

Step1: Rewrite absolute - value inequality

The inequality $30\geq|z + 140|$ is equivalent to $- 30\leq z+140\leq30$.

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

Subtract 140 from all parts of the compound inequality. For the left - hand side: $-30-140\leq z+140 - 140$, which simplifies to $-170\leq z$.

Step3: Solve the right - hand side of the compound inequality

For the right - hand side: $z+140 - 140\leq30 - 140$, which simplifies to $z\leq - 110$.

Answer:

The solution is $-170\leq z\leq - 110$. To graph, click on the endpoints $-170$ and $-110$ to create a line segment with filled - in circles at both endpoints.