Question -
Answer -
Given:
3x – 1 ≥ 5 and x + 2 > –1
Let us consider the first inequality.
3x – 1 ≥ 5
3x – 1 + 1 ≥ 5 + 1
3x ≥ 6
Divide both the sides by 3 we get,
3x/3 ≥ 6/3
x ≥ 2
∴ x ∈ [2, ∞)… (1)
Now, let us consider the second inequality.
x + 2 > –1
x + 2 – 2 > –1 – 2
x > –3
∴ x ∈ (–3, ∞)… (2)
From (1) and (2), we get
x ∈ [2, ∞) ∩ (–3, ∞)
x ∈ [2, ∞)
∴ The solution of the given system of inequations is [2, ∞).