Chapter 3.3, Problem 30PPE

To determine

To solve: the inequality $-12x>132$ . Graph and check the solution.

Answer to Problem 30PPE

  $x<-11$

Explanation of Solution

Given:

The inequality: $-12x>132$

Concept Used:

Let a, b and c be real numbers where $c<0$ . Then,

If $a>b$ , then $\frac{a}{c}<\frac{b}{c}$

Divide both sides of the given inequality by -12 (since, there is a division by a negative number so the sign of the inequality will be reversed),

  $\frac{-12x}{-12}<\frac{132}{-12}$

Simplify both sides of the inequality,

  $x<-11$

Now, to graph the inequality $x<-11$ , draw a number line with an open circle at -11. And since x is strictly less than -11, so draw a line going towards left from the open circle at -11. Thus, the required graph is,

  

Now, to check the above solution, pick any number from the red line section of the above number line and substitute in given inequality,

So, let $x=-20$ . Then,

  $\begin{array}{c}-12\left(-20\right)>132\\ 240>132\end{array}$

Which is a true statement.

Conclusion:

Hence, the solution of the given inequality is $x<-11$ .