Question

solve for r and graph the solution.
\\( \frac { x + 2 } { 1 } > 5 \\) or \\( \frac { x + 1 } { 2 } < 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

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

Step2: Solve the second inequality

Multiply both sides of \(\frac{x + 1}{2}<3\) by \(2\): \(x + 1<6\).
Subtract \(1\) from both sides: \(x<5\).

Answer:

The solution of the compound inequality is \(x < 5\) or \(x>18\). On the number - line, for \(x < 5\), we have an open circle at \(x = 5\) and the line extends to the left. For \(x>18\), we have an open circle at \(x = 18\) and the line extends to the right.