Question

solve for j and graph the solution.
3j + 7 < 19 or $\frac{j + 11}{2} geq 9$
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 7 from both sides of $3j + 7<19$:
$3j+7 - 7<19 - 7$
$3j<12$
Divide both sides by 3:
$j < 4$

Step2: Solve the second inequality

Multiply both sides of $\frac{j + 11}{2}\geq9$ by 2:
$j + 11\geq18$
Subtract 11 from both sides:
$j\geq7$

Answer:

The solution is $j < 4$ or $j\geq7$. On the number - line, there is an open circle at 4 (since $j<4$) and a closed circle at 7 (since $j\geq7$). The graph has a ray pointing to the left from 4 and a ray pointing to the right from 7.