Question

Solve the inequality. Graph and check your solution.

$\frac{x}{-2}\mathbf{+}\mathbf{6}\mathbf{<}\mathbf{-}\mathbf{14}$

Short answer

Solution of the inequality is $x>40$.

Step-by-step solution

Step-1- Solve the inequality

$\frac{x}{-2}+6<-14$

Subtract 6 from both the sides.

$\begin{array}{c}\frac{x}{-2}+6-6<-14-6\\ \frac{x}{-2}<-20\end{array}$

Multiply both sides by -2.

$\begin{array}{c}\frac{x}{-2}\left(-2\right)<-20\left(-2\right)\\ x>40\end{array}$

Step-2- Graph the inequality

The solution of the inequality is $x>40$.

That means, all values$x>40$ 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, $x>40$and substitute in the original inequality and observe the result.

Take$x=42$.

Then,

$\begin{array}{c}\frac{42}{-2}+6<-14\\ -21+6<-14\\ -15<-14\end{array}$

The result$-15<-14$ is true. So, the solution$x>40$ is correct.