ValkyrieRidn
Answered

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Solve the inequality.

[tex]\[ |2x - 2| \ \textgreater \ 4 \][/tex]

[tex]\[ x \ \textless \ [?] \text{ or } x \ \textgreater \ [?] \][/tex]

Sagot :

GinnyAnsweridn
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]
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