Subtracting 9 from both sides, we get–

|3–4x|–9≥0

For this, we have 2 cases,

Case 1:

For this, |3–4x|=3–4x

3–4x–9≥0

–4x–6≥0

4x≤–6

…(1)

Case 2: 0<x<∞

For this, |3–4x|=–(3–4x)

–3+4x–9≥0

4x–12≥0

4x≥12

⇒ x≥3

⇒ xϵ [3, ∞ ) …(2)

(from 1 and 2)

We can verify the answers using graph as well.