Question

solve for z and graph the solution. (\frac{z + 14}{3}<5) or (\frac{3z - 14}{2}>-1) plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first - inequality

Multiply both sides of $\frac{z + 14}{3}<5$ by 3: $z + 14<15$. Then subtract 14 from both sides: $z<15 - 14$, so $z < 1$.

Step2: Solve the second - inequality

Multiply both sides of $\frac{3z-14}{2}>-1$ by 2: $3z-14>-2$. Add 14 to both sides: $3z>-2 + 14$, so $3z>12$. Divide both sides by 3: $z > 4$.

Answer:

The solution of the compound - inequality is $z<1$ or $z > 4$. On the number - line, we have an open circle at $z = 1$ and shade to the left of 1, and an open circle at $z = 4$ and shade to the right of 4.