Question

solve for b and graph the solution.

b - 2 < -7 or b + 3 ≥ 5

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

Add 2 to both sides of $b - 2 < - 7$.
$b-2 + 2< - 7+2$
$b < - 5$

Step2: Solve the second inequality

Subtract 3 from both sides of $b + 3\geq5$.
$b+3 - 3\geq5 - 3$
$b\geq2$

Answer:

The solution is $b < - 5$ or $b\geq2$. On the number - line, there is an open circle at $b=-5$ (since $b < - 5$) and a closed circle at $b = 2$ (since $b\geq2$). The graph has a ray pointing to the left from $b=-5$ and a ray pointing to the right from $b = 2$.