Question

solve the absolute value inequality.
\\(|2x - 2| > 6\\)

select the correct choice below and, if necessary, fill in the answer box to complete your cho

\\(\bigcirc\\) a. the solution set in interval notation is \\(\square\\)
(simplify your answer.)
\\(\bigcirc\\) b. the solution set is \\(\varnothing\\).

Explanation:

Step1: Apply absolute value inequality rule

For \(|a| > b\) (where \(b>0\)), it is equivalent to \(a > b\) or \(a < -b\). So for \(|2x - 2| > 6\), we get two inequalities:
\(2x - 2 > 6\) or \(2x - 2 < -6\)

Step2: Solve \(2x - 2 > 6\)

Add 2 to both sides: \(2x > 6 + 2\)
\(2x > 8\)
Divide by 2: \(x > 4\)

Step3: Solve \(2x - 2 < -6\)

Add 2 to both sides: \(2x < -6 + 2\)
\(2x < -4\)
Divide by 2: \(x < -2\)

Step4: Write in interval notation

The solution is \(x < -2\) or \(x > 4\), which in interval notation is \((-\infty, -2) \cup (4, \infty)\)

Answer:

A. The solution set in interval notation is \((-\infty, -2) \cup (4, \infty)\)