Question

Solve the inequality. Graph your solution.

$\mathbf{3}\mathbf{m}\mathbf{-}\mathbf{8}\mathbf{>}\mathbf{-}\mathbf{30}\mathbf{+}\mathbf{5}\mathbf{m}$

Short answer

Solution of the inequality is $m<11$.

Step-by-step solution

Step 1. Solve the inequality

$3m-8>-30+5m$

Subtract 5m and add 8 both the sides.

$\begin{array}{c}3m-8+8-5m>-30+5m+8-5m\\ -2m>-22\end{array}$

Divide both sides by -2.

$\begin{array}{c}m<\frac{-22}{-2}\\ m<11\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $m<11$.

That means, all values $m<11$ 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, $m<11$ and substitute in the original inequality and observe the result.

Take $m=11$.

Then,

$\begin{array}{c}3\times 0-8>-30+5\times 0\\ 0-8>-30+0\\ -8>-30\end{array}$

The result $-8>-30$ is true. So, the solution $m<11$ is correct.