Solve each of the following system of inequations in R
5x – 1 < 24, 5x + 1 > –24
Given 5x – 1 < 24 and 5x + 1 > –24
Let us consider the first inequality.
5x – 1 < 24
⇒ 5x – 1 + 1 < 24 + 1
⇒ 5x < 25
⇒ x < 5
∴ x ∈ (–∞, 5) (1)
Now, let us consider the second inequality.
5x + 1 > –24
⇒ 5x + 1 – 1 > –24 – 1
⇒ 5x > –25
⇒ x > –5
∴ x ∈ (–5, ∞) (2)
From (1) and (2), we get
x ∈ (–∞, 5) ∩ (–5, ∞)
∴ x ∈ (–5, 5)
Thus, the solution of the given system of inequations is (–5, 5).