Chapter 3.3, Problem 29PPE

To determine

To solve: the inequality $63\ge 7q$ . Graph and check the solution.

Answer to Problem 29PPE

  $q\le 9$

Explanation of Solution

Given:

The inequality: $63\ge 7q$

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 7,

  $\frac{63}{7}\ge \frac{7q}{7}$

Simplify both sides of the inequality,

  $9\ge q$

Now, to graph the inequality $q\le 9$ , draw a number line with a closed circle at 9. And since q is less than or equal to 8, so draw a line going towards left from the closed circle at 9. 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 $q=0$ . Then,

  $\begin{array}{c}63\ge 7\left(0\right)\\ 63\ge 0\end{array}$

Which is a true statement.

Conclusion:

Hence, the solution of the given inequality is $q\le 9$ .