Given,
|3-4x| ≥ 9
Subtracting 9 from both sides, we get–
|3–4x| – 9 ≥ 0
For this, we have 2 cases,
Case 1 : - ∞ < x < \(\frac{3}{4}\)
For this,
|3 – 4x| = 3 – 4x
3 – 4x – 9 ≥ 0
–4x–6 ≥ 0
4x ≤ –6
x ≤ \(-\frac{3}{2}\)
⇒ x ∈ (-∞,\(-\frac{3}{2}\)] …(1)
Case 2 : 0 < x < ∞
For this,
|3–4x| = –(3–4x)
–3+4x–9 ≥ 0
4x–12 ≥ 0
4x ≥ 12
⇒ x ≥ 3
⇒ x∈ [3, ∞ ) …(2)
x ∈ (-∞,\(-\frac{3}{2}\)] ∪ [3,∞) (from 1 and 2)
We can verify the answers using graph as well.
