Question

Solve each inequality. Check your solution.

$\mathbf{-}\mathbf{9}\mathit{m}\mathbf{<}\mathbf{-}\mathbf{36}$

Short answer

The solution of the given inequality$-9m<-36$ is $\mathit{m}\mathbf{>}\mathbf{4}$.

Step-by-step solution

Step 1. Write the division property of inequalities.

The division property of inequalities states that if both sides of the inequality are divided by a positive number the sign of the inequality remains the same and if both sides of the inequality are divided by a negative number then the sign of the inequality changes that is:

1. If $a>b$and $c$is a positive number then $\frac{a}{c}>\frac{b}{c}$.
2. If $a<b$and $c$is a positive number then $\frac{a}{c}<\frac{b}{c}$.
3. If $a>b$and $c$is a negative number then $\frac{a}{c}<\frac{b}{c}$.
4. If $a<b$and $c$is a negative number then $\frac{a}{c}>\frac{b}{c}$.

Step 2. Solve the given inequality −9m<−36.

The solution of the given inequality$-9m<-36$ is:

$\begin{array}{c}-9m<-36\\ \frac{-9m}{-9}>\frac{-36}{-9}\left(\text{byusingdivisionpropertyofinequality}\right)\\ m>4\end{array}$

Therefore, the solution of the given inequality$-9m<-36$ is $m>4$.

Step 3. Check the solution.

To perform the check of the solution, substitute a number greater than 4 as$m>4$ in the given inequality $-9m<-36$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $m=5$, as $5>4$.

Now substitute 5 for $m$in the inequality $-9m<-36$.

$\begin{array}{c}-9m<-36\\ -9\left(5\right)<-36\\ -45<-36\end{array}$

As, the condition obtained$-45<-36$ is true, therefore the solution is correct.