Question

solve for u and graph the solution.
\frac{-2u + 3}{3} \geq 5 or -4u - 17 \leq 3
plot the endpoints. select an endpoint to change it from closed to open. select the a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Multiply both sides of \(\frac{-2u + 3}{3}\geq5\) by \(3\): \(-2u+3\geq15\).
Subtract \(3\) from both sides: \(-2u\geq12\).
Divide both sides by \(- 2\) and reverse the inequality sign: \(u\leq - 6\).

Step2: Solve the second inequality

Add \(17\) to both sides of \(-4u-17\leq3\): \(-4u\leq20\).
Divide both sides by \(-4\) and reverse the inequality sign: \(u\geq - 5\).

Answer:

The solution is \(u\leq - 6\) or \(u\geq - 5\). On the number - line, for \(u\leq - 6\), we have a ray starting from \(-6\) (closed circle since the inequality is \(\leq\)) and going to the left. For \(u\geq - 5\), we have a ray starting from \(-5\) (closed circle since the inequality is \(\geq\)) and going to the right.