Question

Solve: 4|X - 2| > 5. Write your solution in interval notation. a) x < -1 or x > 3 b) x < 3 or x > 7 c) x < 1 or x > 5 d) x < -3 or x > 1

Answer 1

The solution in interval notation is x < -1 or x > 3.

Option (a) is true.

Explanation:

To solve the inequality 4|X - 2| > 5, we can break it down into two cases:

Case 1: X - 2 > 0

In this case, the absolute value can be removed, and the inequality becomes:

4(X - 2) > 5

Simplifying, we have:

4X - 8 > 5

4X > 13

X > 13/4

Case 2: X - 2 < 0

In this case, the absolute value becomes the negative of its argument, and the inequality becomes:

4(-X + 2) > 5

-4X + 8 > 5

-4X > -3

X < 3/4

Combining the results from both cases, we have:

X < 3/4 or X > 13/4

Rewriting the solution in interval notation, we express the solution as:

(-∞, 3/4) U (13/4, ∞)

Therefore,

Option (a) is true.