Question

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

Answer 1

Answer:

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

Step-by-step 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 $(-\infty,-4] \cup[12, \infty)$.