Question -
Answer -
Given:
x – 2 > 0 and 3x < 18
Let us consider the first inequality.
x – 2 > 0
x – 2 + 2 > 0 + 2
x > 2
∴ x ∈ ( 2, ∞) …(1)
Now, let us consider the second inequality.
3x < 18
Divide both the sides by 3 we get,
3x/3 < 18/3
x < 6
∴ x ∈ (–∞, 6) …(2)
From (1) and (2), we get
x ∈ (2, ∞) ∩ (–∞, 6)
x ∈ ( 2, 6)
∴ The solution of the given system of inequations is (2, 6).