Question -
Answer -
Given:
3x – 6 > 0 and 2x – 5 > 0
Let us consider the first inequality.
3x – 6 > 0
3x – 6 + 6 > 0 + 6
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.
2x – 5 > 0
2x – 5 + 5 > 0 + 5
2x > 5
Divide both the sides by 2 we get,
2x/2 > 5/2
x > 5/2
∴ x ∈ (5/2, ∞)… (2)
From (1) and (2), we get
x ∈ (2, ∞) ∩ (5/2, ∞)
x ∈ (5/2, ∞)
∴ The solution of the given system of inequations is (5/2, ∞).