Chapter 3.3, Problem 20PPE

To determine

To solve: the inequality $4t<-12$ . Graph and check the solution.

Answer to Problem 20PPE

  $t<-3$

  

Explanation of Solution

Given:

The inequality: $4t<-12$

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 4,

  $\frac{4t}{4}<\frac{-12}{4}$

Simplify both sides of the inequality,

  $t<-3$

Now, to graph the inequality $t<-3$ , draw a number line with an open circle at -3. And since t is strictly less than -3, so draw a line going towards left from the open circle at -3. 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 $t=-4$ . Then,

  $\begin{array}{c}4\left(-4\right)<-12\\ -16<-12\end{array}$

Which is a true statement.

Conclusion:

Hence, the solution of the given inequality is $t<-3$ .