Chapter 1.7, Problem 50E

To determine

To calculate: The solution of the inequality $\left|x-8\right|\ge 0$ and graph the solution set.

The solution set of the inequality $\left|x-8\right|\ge 0$ is all real numbers.

Calculation:

The inequality is $\left|x-8\right|\ge 0$.

Use Absolute Value Inequality property, which says that $\left|u\right|\ge a$ if and only if $u\le -a$ or $u\ge a$

$\begin{array}{l}x-8\ge 0\text{ or }\left(x-8\right)\le -0\\ x-8\ge 0\text{ or }\left(x-8\right)\le 0\end{array}$

Add 8 to each part with property of addition of the constant of the Inequality, which says that if $a<b$, then $a<b$ becomes $a+c<b+c$.

$x\ge 8\text{ or }x\le 8$

So, the solution set of the given inequality is all real numbers that are greater than or equal to $8$ and less than or equal to $8$, denoted by $\left(-\infty ,8\right]\cup \left[8,\infty \right)$ which means all real number

Graph:

The graph of the solution set is shown as:

All the points on the number line are included in the solution set.