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

4