Question

Write an absolute value inequality whose solution set is shown by the graphs. Each mark on the graph represents a whole number.  (Your answers will have the absolute value symbols, | |.)

Answer 1

To answer this question we will use the following:

$\begin{gathered} |a|\ge b\text{ if and only if} \\ a\ge b\text{ or }a\le-b. \end{gathered}$

Notice that the given set consists of the real numbers that are greater than or equal to 3 or that are less than or equal to -3, the above statement in algebraic notation is:

$x\geq3\text{ or }x\leq-3.$

Using the first equations we get that the given set can be represented by the following absolute value inequality:

$|x|\ge3.$

Answer:

$|x|\ge3.$