Chapter 3.3, Problem 28PPE

To determine

To solve: the inequality $8t\le 64$ . Graph and check the solution.

Answer to Problem 28PPE

  $t\le 8$

Explanation of Solution

Given:

The inequality: $8t\le 64$

Concept Used:

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

If $a\le b$ , then $\frac{a}{c}\le \frac{b}{c}$

Divide both sides of the given inequality by 18,

  $\frac{8t}{8}\le \frac{64}{8}$

Simplify both sides of the inequality,

  $t\le 8$

Now, to graph the inequality $t\le 8$ , draw a number line with a closed circle at 8. And since t is less than or equal to 8, so draw a line going towards left from the closed circle at 8. 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 $t=0$ . Then,

  $\begin{array}{c}8\left(0\right)\le 64\\ 0\le 64\end{array}$

Which is a true statement.

Conclusion:

Hence, the solution of the given inequality is $t\le 8$ .