Question

solve for z and graph the solution. |z + 7| + 9 > 12 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: Isolate the absolute - value expression

Subtract 9 from both sides of the inequality $|z + 7|+9>12$.
$|z + 7|>12 - 9$
$|z + 7|>3$

Step2: Consider two cases

Case 1: $z + 7>3$.
Subtract 7 from both sides: $z>3 - 7$, so $z>-4$.
Case 2: $z + 7<-3$.
Subtract 7 from both sides: $z<-3 - 7$, so $z<-10$.

Answer:

The solution is $z<-10$ or $z>-4$. On the number - line, there is an open circle at $z = - 10$ with an arrow pointing to the left and an open circle at $z=-4$ with an arrow pointing to the right.