Q. 13 PT - Algebra 1

Question

Solve each compound inequality. Then graph the solution set.

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

Step-by-Step Solution

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 1. Solve the given compound inequality − 11 ≤ 2 h − 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: