Question

solve for u and graph the solution.
\\(\frac{3u + 2}{4}\geq5\\) or \\(\frac{u - 10}{4}\leq - 3\\)
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

Solve $\frac{3u + 2}{4}\geq5$. Multiply both sides by 4: $3u+2\geq20$. Then subtract 2 from both sides: $3u\geq18$. Divide both sides by 3: $u\geq6$.

Step2: Solve the second - inequality

Solve $\frac{u - 10}{4}\leq - 3$. Multiply both sides by 4: $u - 10\leq - 12$. Then add 10 to both sides: $u\leq - 2$.

Step3: Graph the solutions

For $u\geq6$, we have a closed - circle at 6 and a ray going to the right. For $u\leq - 2$, we have a closed - circle at - 2 and a ray going to the left.

Answer:

The solution of the compound inequality is $u\leq - 2$ or $u\geq6$. On the number - line, we have a ray starting from $u=-2$ (closed - circle) and going to the left and a ray starting from $u = 6$ (closed - circle) and going to the right.