Chapter 2.3, Problem 23E

To determine

To graph:

The solution set for the following inequalities:

  $2\le -\frac{2}{9}x$

Explanation of Solution

Given information:

  $2\le -\frac{2}{9}x$

Graph:

Interpretation:

The given inequality equation is:

  $2\le -\frac{2}{9}x$

Switch sides:

  $\begin{array}{l}2\le -\frac{2}{9}x\\ -\frac{2}{9}x\ge 2\end{array}$

Now multiply by $-\frac{9}{2}$ on the both sides of above equation:

  $\begin{array}{l}-\frac{2}{9}x\ge 2\\ -\frac{2}{9}\times -\frac{9}{2}x\ge 2\times -\frac{9}{2}\\ x\ge -9\end{array}$

So, the solution set of $x\ge -9$ is graphed as above.