Question

Solve each compound inequality. Then graph the solution set.

$\mathbf{-}\mathbf{11}\mathbf{\le }\mathbf{2}\mathit{h}\mathbf{-}\mathbf{5}\mathbf{\le }\mathbf{13}$

Short answer

The solution of the given compound inequality $-11\le 2h-5\le 13$is $\mathit{h}\mathbf{\in }\left[-3,9\right]$.

The graph of the solution set which is$h\in \left[-3,9\right]$ is:

Step-by-step solution

Step 1. Solve the given compound inequality −11≤2h−5≤13.

The solution of the given compound inequality$-11\le 2h-5\le 13$ is:

$\begin{array}{c}-11\le 2h-5\le 13\\ -11+5\le 2h-5+5\le 13+5\\ -6\le 2h\le 18\\ \frac{-6}{2}\le \frac{2h}{2}\le \frac{18}{2}\\ -3\le h\le 9\\ h\in \left[-3,9\right]\end{array}$

Therefore, the solution of the compound inequality$-11\le 2h-5\le 13$ is $h\in \left[-3,9\right]$.

Step 2. Draw the graph of the solution set which is h∈[−3,9].

The graph of the solution set which is$h\in \left[-3,9\right]$ is: