Question

solve for b and graph the solution. 5b + 12 ≥ 12 or b + 20 < 12. 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

Subtract 12 from both sides of $5b + 12\geq12$.
$5b+12 - 12\geq12 - 12$
$5b\geq0$
Divide both sides by 5: $b\geq0$.

Step2: Solve the second inequality

Subtract 20 from both sides of $b + 20<12$.
$b+20 - 20<12 - 20$
$b<-8$.

Answer:

The solution is $b\geq0$ or $b < - 8$. On the number - line, we have an open circle at $b=-8$ (since $b < - 8$) and a closed circle at $b = 0$ (since $b\geq0$). The graph has a ray going to the left from $b=-8$ and a ray going to the right from $b = 0$.