Chapter 3.3, Problem 13PPE

To determine

To solve: the given inequality and graph the solution. Check the result.

Answer to Problem 13PPE

The solution is $x\ge -3$ .

Explanation of Solution

Given information:

Given inequality

  $-7\le \frac{7}{3}x$

Calculation:

First solve the inequality $-7\le \frac{7}{3}x$ . Then

  $\begin{array}{c}-7\le \frac{7}{3}x\\ \frac{3}{7}\left(-7\right)\le \frac{3}{7}\left(\frac{7}{3}\right)x\\ -3\le x\\ x\ge -3\end{array}$

It is to be draw the graph of $x\ge -3$ . Now $x\ge -3$ means all real numbers $x$ that are greater than or equal to $-3$ . Since $-3$ is a solution, draw a closed dot at $-3$ . The numbers greater than $-3$ are to the right of $-3$ on the number line. Shade to the right of $-3$ . Therefore, the graph is

  

To check the inequality symbol of $x\ge -3$ , ,make sure that a number greater than $-3$ is a solution of the original inequality. To check this substitute $x=0$ into the original inequality.

Therefore,

  $\begin{array}{l}-7\le \frac{7}{3}\times 0\\ -7\le 0\end{array}$

To check endpoint $-3$ of $x\ge -3$ , make sure that $-3$ is a solution of the related equation

  $\begin{array}{l}-7=\frac{7}{3}x\\ -7=\frac{7}{3}\left(-3\right)\\ -7=-7\end{array}$

Hence the solution is $x\ge -3$ .