Question -
Answer -
Given:
5x – 1 < 24 and 5x + 1 > –24
Let us consider the first inequality.
5x – 1 < 24
5x – 1 + 1 < 24 + 1
5x < 25
Divide both the sides by 5 we get,
5x/5 < 25/5
x < 5
∴ x ∈ (–∞, 5)… (1)
Now, let us consider the second inequality.
5x + 1 > –24
5x + 1 – 1 > –24 – 1
5x > –25
Divide both the sides by 5 we get,
5x/5 > -25/5
x > -5
∴ x ∈ (–5, ∞)… (2)
From (1) and (2), we get
x ∈ (–∞, 5) ∩ (–5, ∞)
x ∈ (–5, 5)
∴ The solution of the given system of inequations is (–5, 5).