Question

solve for b and graph the solution.
7b + 12 ≤ 12 or $\frac{3b + 11}{4} geq 5$
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

Subtract 12 from both sides of $7b + 12\leq12$.
$7b+12 - 12\leq12 - 12$
$7b\leq0$
Divide both sides by 7: $b\leq0$

Step2: Solve the second inequality

Multiply both sides of $\frac{3b + 11}{4}\geq5$ by 4.
$3b + 11\geq20$
Subtract 11 from both sides: $3b\geq20 - 11$
$3b\geq9$
Divide both sides by 3: $b\geq3$

Answer:

The solution is $b\leq0$ or $b\geq3$. On the number - line, a closed circle at 0 with an arrow pointing to the left and a closed circle at 3 with an arrow pointing to the right.