Question

For the following exercises, solve each inequality and write the solution in interval notation.

32. | x − 4 | ≥ 8

Answer 1

The solution of the given set in interval form is
`$(-\infty,-4] \cup[12, \infty)$`.

Explanation:

It is given in the question an inequality as
`$|x-4| \geq 8$`.

It is required to determine the solution of the inequality.

To determine the solution of the inequality, solve the inequality
`$x-4 \geq 8$` and,
`$x-4 \leq-8$`

Step 1 of 2

Solve the inequality
`$x-4 \geq 8$`

`$$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$$`

Solve the inequality
`$x-4 \leq-8$`.

`$$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$$`

Step 2 of 2

The common solution from the above two solutions is x less than -4 and
`$x \geq 12$`.

The solution set in terms of interval is
`$(-\infty,-4] \cup[12, \infty)$`.