Question

solve for x and graph the solution.

\\( \frac { 3 x + 2 } { 4 } > 2 \\) or \\( \frac { x - 5 } { 4 } \leq - 2 \\)

plot the endpoints. select an endpoint to change it from closed to open. s
a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Multiply both sides of \(\frac{3x + 2}{4}>2\) by \(4\): \(3x+2>8\).
Subtract \(2\) from both sides: \(3x>6\).
Divide both sides by \(3\): \(x > 2\).

Step2: Solve the second inequality

Multiply both sides of \(\frac{x - 5}{4}\leq-2\) by \(4\): \(x-5\leq - 8\).
Add \(5\) to both sides: \(x\leq - 3\).

Answer:

The solution is \(x\leq - 3\) or \(x > 2\). On the number - line, for \(x\leq - 3\), we have a closed circle at \(x = - 3\) (since the inequality includes equality) and the ray goes to the left. For \(x>2\), we have an open circle at \(x = 2\) (since the inequality does not include equality) and the ray goes to the right.