Chapter EP, Problem 1.6.17EP

To determine

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

Answer to Problem 1.6.17EP

Therequired solution is $x<\frac{3}{2},x>-1$ and the graph is shown in Figure 1

Explanation of Solution

Given:

Thegiven inequalityis,

  $\left|4x-1\right|<5$

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,

  $\left|4x-1\right|<5$

Consider the inequality is solved as,

  $\begin{array}{l}4x-1<5\\ 4x<6\\ x<\frac{3}{2}\end{array}$ or $\begin{array}{l}4x-1>-5\\ 4x>-4\\ x>-1\end{array}$

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

Figure 1