Question

Solve the inequality. Graph your solution.

$\frac{\mathbf{-}\mathbf{5}\mathbf{s}\mathbf{-}\mathbf{8}}{\mathbf{4}}\ge \mathbf{-}\mathbf{22}$

Short answer

Solution of the inequality is $s\le 16$.

Step-by-step solution

Step 1. Solve the inequality

$\frac{-5s-8}{4}\ge -22$

Multiply both sides by 4.

$\begin{array}{c}\frac{-5s-8}{4}\times 4\ge -22\times 4\\ -5s-8\ge -88\end{array}$

Add 8 on both sides.

$\begin{array}{c}-5s-8+8\ge -88+8\\ -5s\ge -80\end{array}$

Divide both sides by -5.

$\begin{array}{c}s\le \frac{-80}{-5}\\ s\le 16\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $s\le 16$.

That means, all values $s\le 16$ satisfy the inequality. So, the graph can be given as shown below.

Step 3. Check the solution

To check the solution, take any random number, $s\le 16$ and substitute in the original inequality and observe the result.

Take $x=1$.

Then,

$\begin{array}{c}\frac{-5\times 0-8}{4}\ge -22\\ \frac{0-8}{4}\ge -22\\ \frac{-8}{4}\ge -22\\ -2\ge -22\end{array}$

The result $-2\ge -22$ is true. So, the solution $s\le 16$ is correct.