Chapter 12, Problem 44CUR

To determine

To solve : The inequality, graph and check the solution.

Answer to Problem 44CUR

The solution is $x>8$ . i.e. all the numbers greater than $8$ is the solution.

Explanation of Solution

Given information : $-2x<-16$

Formula used : Dividing each side of an inequality by a positive number produces an equivalent inequality.

Dividing each side of an inequality by a negative numbers and reversing the direction of the inequality symbol produces an equivalent inequality.

Calculation :

$\begin{array}{l}-2x<-16\\ \frac{-2x}{-2}>\frac{-16}{-2}\\ x>8\end{array}$ [Divide each side by $\left(-2\right)$ ]

Check:

$10$ is the number greater than $8$ . Putting $10$ on the place of $x$ in the left hand side of the given inequality we get,

  $\begin{array}{c}-2x=\left(-2\right)\times 10\\ =-20\end{array}$

  $-20<-16$

Therefore, the solution is right.

Graph :

The solution is $x>8$ .

Interpretation : The solution is $x>8$ . i.e. all the numbers greater than $8$ is the solution.