Question

solve for q and graph the solution.
$\frac{q + 18}{3}leq6$ or $5q-19geq1$
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 $\frac{q + 18}{3}\leq6$ by 3: $q + 18\leq18$. Then subtract 18 from both sides: $q\leq0$.

Step2: Solve the second inequality

Add 19 to both sides of $5q-19\geq1$: $5q\geq20$. Divide both sides by 5: $q\geq4$.

Step3: Graph - endpoints

For $q\leq0$, the endpoint is 0 (closed - circle since $\leq$). For $q\geq4$, the endpoint is 4 (closed - circle since $\geq$). The solution set is $q\leq0$ or $q\geq4$. On the number - line, we have a ray going to the left from 0 (including 0) and a ray going to the right from 4 (including 4).

Answer:

The solution of the inequality is $q\leq0$ or $q\geq4$. On the number - line, place a closed circle at 0 and draw a ray to the left, and place a closed circle at 4 and draw a ray to the right.