Given as
2x + 6 ≥ 0 and 4x – 7 < 0
Now, let us consider the first inequality.
2x + 6 ≥ 0
2x + 6 – 6 ≥ 0 – 6
2x ≥ –6
Dividing both the sides by 2 we get,
2x/2 ≥ -6/2
x ≥ -3
∴ x ∈ [–3, ∞) …(1)
Then, let us consider the second inequality.
4x – 7 < 0
4x – 7 + 7 < 0 + 7
4x < 7
Dividing both the sides by 4 we get,
4x/4 < 7/4
x < 7/4
∴ x ∈ [–∞, 7/4) …(2)
From (1) and (2), we get
x ∈ (-3, ∞) ∩ (–∞, 7/4)
x ∈ (-3, 7/4)
∴ The solution of the given system of inequations is (-3, 7/4).
