Question

Solve | 4x – 3 | ≥ 5.

Answer 1

Solve | 4x – 3 | ≥ 5

⇒ 4x – 3 ≥ 5 or – (4x – 3) ≥ 5, i.e., 4x – 3 ≤ –5 

⇒ 4x ≥ 8 or 4x ≤ –2 ⇒ x ≥ 2 or x ≤ \(-\frac12\)

⇒ Solution set = \(\bigg\{\)x | x ≥ 2 or x ≤ \(-\frac12\)\(\bigg\}\) = (-∞, \(-\frac12\)] ∪ [2, ∞)