Question -
Answer -
Given:
2x – 3 < 7 and 2x > –4
Let us consider the first inequality.
2x – 3 < 7
2x – 3 + 3 < 7 + 3
2x < 10
Divide both the sides by 2 we get,
2x/2 < 10/2
x < 5
∴ x ∈ ( –∞, 5)… (1)
Now, let us consider the second inequality.
2x > –4
Divide both the sides by 2 we get,
2x/2 > -4/2
x > –2
∴ x ∈ (–2, ∞)… (2)
From (1) and (2), we get
x ∈ (–∞, 5) ∩ (–2, ∞)
x ∈ (–2, 5)
∴ The solution of the given system of inequations is (–2, 5).