Given 4x – 1 ≤ 0 and 3 – 4x < 0

Let us consider the first inequality.

4x – 1 ≤ 0

⇒ 4x – 1 + 1 ≤ 0 + 1

⇒ 4x ≤ 1

(1)

Now, let us consider the second inequality.

3 – 4x < 0

⇒ 3 – 4x – 3 < 0 – 3

⇒ –4x < –3

(2)

From (1) and (2), we get

∴ x ∈ ∅

Thus, there is no solution of the given system of inequations.