Question

solve the compound inequality and graph the solution set.
-11 < 2x - 5 < -1
graph
solution

Explanation:

Step1: Solve the compound inequality

Given \(-11 < 2x - 5 < -1\).
First, add \(5\) to all parts of the inequality:
\(-11+5 < 2x-5 + 5 < -1 + 5\)
\(-6 < 2x < 4\).
Then divide all parts by \(2\):
\(\frac{-6}{2}<\frac{2x}{2}<\frac{4}{2}\)
\(-3 < x < 2\).

Step2: Analyze the graph

For the inequality \(-3 < x < 2\), on a number - line, we have an open circle at \(x=-3\) (because \(x
eq - 3\)) and an open circle at \(x = 2\) (because \(x
eq2\)), and the line segment between them is shaded.

Answer:

The solution is \(-3 < x < 2\). The correct graph is the one with an open circle at \(-3\), an open circle at \(2\), and the line segment between them shaded.