Let's solve the inequality [tex]\(|2x - 2| > 4\)[/tex].
### Step-by-Step Solution
1. Understand the Absolute Value Inequality:
[tex]\[
|2x - 2| > 4
\][/tex]
The inequality [tex]\(|A| > B\)[/tex] translates to two cases:
- [tex]\(A > B\)[/tex]
- [tex]\(A < -B\)[/tex]
Here, [tex]\(A = 2x - 2\)[/tex] and [tex]\(B = 4\)[/tex]. Thus, we have:
- [tex]\(2x - 2 > 4\)[/tex]
- [tex]\(2x - 2 < -4\)[/tex]
2. Solve Each Case Separately:
- For [tex]\(2x - 2 > 4\)[/tex]:
[tex]\[
2x - 2 > 4
\][/tex]
Add 2 to both sides:
[tex]\[
2x > 6
\][/tex]
Divide by 2:
[tex]\[
x > 3
\][/tex]
- For [tex]\(2x - 2 < -4\)[/tex]:
[tex]\[
2x - 2 < -4
\][/tex]
Add 2 to both sides:
[tex]\[
2x < -2
\][/tex]
Divide by 2:
[tex]\[
x < -1
\][/tex]
3. Combine the Solutions:
The solution to the inequality [tex]\(|2x - 2| > 4\)[/tex] is:
- [tex]\(x < -1\)[/tex]
- [tex]\(x > 3\)[/tex]
### Final Answer
The values of [tex]\(x\)[/tex] that satisfy the inequality [tex]\(|2x - 2| > 4\)[/tex] are:
[tex]\[
x < -1 \quad \text{or} \quad x > 3
\][/tex]
