Question

1. |2x - 4| > 6

Explanation:

Step1: Apply absolute value inequality rule

For \(|A| > B\) (where \(B>0\)), it is equivalent to \(A > B\) or \(A < -B\). So for \(|2x - 4| > 6\), we get two inequalities:
\(2x - 4 > 6\) or \(2x - 4 < -6\)

Step2: Solve \(2x - 4 > 6\)

Add 4 to both sides: \(2x - 4 + 4 > 6 + 4\)
Simplify: \(2x > 10\)
Divide both sides by 2: \(\frac{2x}{2} > \frac{10}{2}\)
We get: \(x > 5\)

Step3: Solve \(2x - 4 < -6\)

Add 4 to both sides: \(2x - 4 + 4 < -6 + 4\)
Simplify: \(2x < -2\)
Divide both sides by 2: \(\frac{2x}{2} < \frac{-2}{2}\)
We get: \(x < -1\)

Answer:

The solution to the inequality \(|2x - 4| > 6\) is \(x < -1\) or \(x > 5\)