Question

Solve the inequality |2x - 4| > 2.

a) x < 1 or x > 3
b) x > 1 and x < 3
c) x > 1 or x < 3
d) x < 1 and x > 3

Answer 1

To solve the inequality |2x - 4| > 2, consider two cases: (2x - 4) > 2 and -(2x - 4) > 2. Solve for x in each case and find that x < 1 or x > 3.

Step-by-step explanation:

To solve the inequality |2x - 4| > 2, we need to consider two cases:

1. Case 1: (2x - 4) > 2. In this case, we solve for x by adding 4 to both sides of the inequality, giving us 2x > 6. Then we divide both sides by 2, giving us x > 3.
2. Case 2: -(2x - 4) > 2. In this case, we solve for x by multiplying both sides of the inequality by -1, giving us 2x - 4 < -2. Then we add 4 to both sides, giving us 2x < 2. Finally, we divide both sides by 2, giving us x < 1.

Therefore, the solution to the inequality |2x - 4| > 2 is x < 1 or x > 3. So the correct answer is (a) x < 1 or x > 3.