Answer:
The solution of the given set in interval form is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].
Step-by-step explanation:
It is given in the question an inequality as [tex]$|x-4| \geq 8$[/tex].
It is required to determine the solution of the inequality.
To determine the solution of the inequality, solve the inequality [tex]$x-4 \geq 8$[/tex] and, [tex]$x-4 \leq-8$[/tex]
Step 1 of 2
Solve the inequality [tex]$x-4 \geq 8$[/tex]
[tex]$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$[/tex]
Solve the inequality [tex]$x-4 \leq-8$[/tex].
[tex]$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$[/tex]
Step 2 of 2
The common solution from the above two solutions is x less than -4 and [tex]$x \geq 12$[/tex].
The solution set in terms of interval is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].
