Chapter EP, Problem 1.6.20EP

To determine

To Find: The solution for the inequality and graph for it on the number line.

Answer to Problem 1.6.20EP

Therequired solution is $w\ge \frac{12}{5},w\le \frac{-6}{5}$ and the graph is shown in Figure 1

Explanation of Solution

Given:

Thegiven inequalityis,

  $\left|5w-3\right|\ge 9$

Calculation:

Consider the absolute value of $x$ is,

  $\left|x\right|=\{\begin{array}{l}x,\text{if}x\ge 0\\ -x,\text{if}x<0\end{array}$

Consider the given inequality is,

  $\left|5w-3\right|\ge 9$

Consider the inequality is solved as,

  $\begin{array}{l}5w-3\ge 9\\ 5w\ge 12\\ w\ge \frac{12}{5}\end{array}$ or $\begin{array}{l}5w-3\le -9\\ 5w\le -6\\ w\le \frac{-6}{5}\end{array}$

The graph of the inequality on the number line is shown in Figure 1

Figure 1