Question

Solve |3 – 4x| ≥ 9.

Answer 1

We have |3 – 4x| ≥ 9

⇒ 3 – 4x ≤ –9 or 3 – 4x ≥ 9   .....(Since |x| ≥ a ⇒ x ≤ –a or x ≥ a)

⇒ –4x ≤ –12 or –4x ≥ 6

⇒ x ≥ 3 or x ≤ `(-3)/2`   .....(Dividing both sides by –4)

⇒ x ∈ (`-oo, (-3)/2`] ∪ [`3, oo`)