Question

solve for r and graph the solution.
\\( \frac { 3 r + 2 } { 4 } > 5 \\) or \\( \frac { 3 r + 1 } { 2 } < 5 \\)
plot the endpoints. select an endpoint to change it from closed to open. select th
a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Multiply both sides of \(\frac{3r + 2}{4}>5\) by \(4\): \(3r+2>20\).
Subtract \(2\) from both sides: \(3r>18\).
Divide both sides by \(3\): \(r > 6\).

Step2: Solve the second inequality

Multiply both sides of \(\frac{3r + 1}{2}<5\) by \(2\): \(3r + 1<10\).
Subtract \(1\) from both sides: \(3r<9\).
Divide both sides by \(3\): \(r<3\).

Answer:

The solution is \(r < 3\) or \(r>6\). On the number - line, for \(r < 3\), we have an open - circle at \(r = 3\) and a ray extending to the left. For \(r>6\), we have an open - circle at \(r = 6\) and a ray extending to the right.