Solve: | 4 x − 1 | ≥ 4 Give your answer as using interval notation, with integers or fractions.

Answer 1

|4x - 1| >= 4

Part 1 (Positive Half)

4x - 1 >= 4

4x >= 5

x >= 5/4

Part 2 (Negative Half with inequality flipped)

4x - 1 <= -4

4x <= -3

x <= -3/4

(-inf, -3/4] or [5/4, inf)

Answer 2

I. Assuming 4x - 1 ≥ 0

4x - 1 ≥ 4

4x ≥ 5

x ≥ 5/4

II. Assuming 4x - 1 < 0

-(4x - 1) ≥ 4

-4x + 1 ≥ 4

-4x ≥ 3

x ≤ -3/4