Solve each of the following system of inequations in R
4x – 1 ≤ 0, 3 – 4x < 0
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.
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