Question

solve for k and graph the solution

5k + 8 ≤ 3 or 3k - 11 > 1

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 \(5k + 8\leq3\)

Subtract \(8\) from both sides: \(5k\leq3 - 8\), so \(5k\leq - 5\).
Divide both sides by \(5\): \(k\leq - 1\).

Step2: Solve \(3k-11>1\)

Add \(11\) to both sides: \(3k>1 + 11\), so \(3k>12\).
Divide both sides by \(3\): \(k>4\).

Answer:

The solution of the compound - inequality is \(k\leq - 1\) or \(k>4\). On the number - line, we plot a closed circle at \(k = - 1\) (since the inequality \(k\leq - 1\) includes equality) and shade to the left of \(k=-1\). We plot an open circle at \(k = 4\) (since the inequality \(k>4\) does not include equality) and shade to the right of \(k = 4\).