Solve each of the following system of inequations in R
2x + 6 ≥ 0, 4x – 7 < 0
Given 2x + 6 ≥ 0 and 4x – 7 < 0
Let us consider the first inequality.
2x + 6 ≥ 0
⇒ 2x + 6 – 6 ≥ 0 – 6
⇒ 2x ≥ –6
⇒ x ≥ –3
∴ x ∈ [–3, ∞) (1)
Now, let us consider the second inequality.
4x – 7 < 0
⇒ 4x – 7 + 7 < 0 + 7
⇒ 4x < 7
(2)
From (1) and (2), we get
Thus, the solution of the given system of inequations is
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