Question

solve for w and graph the solution.
\\( \frac { 2 w + 1 } { 3 } \geq 5 \\) or \\( w + 11 \leq 17 \\)
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 \(\frac{2w + 1}{3}\geq5\) by \(3\): \(2w+1\geq15\).
Subtract \(1\) from both sides: \(2w\geq14\).
Divide both sides by \(2\): \(w\geq7\).

Step2: Solve the second inequality

Subtract \(11\) from both sides of \(w + 11\leq17\): \(w\leq6\).

Answer:

The solution is \(w\leq6\) or \(w\geq7\). On the number - line, we have a closed circle at \(w = 6\) (since the inequality \(w\leq6\) includes \(6\)) and a closed circle at \(w = 7\) (since the inequality \(w\geq7\) includes \(7\)). The graph consists of two parts: a ray to the left of \(6\) (including \(6\)) and a ray to the right of \(7\) (including \(7\)).