Question -
Answer -
Given:
11 – 5x > –4 and 4x + 13 ≤ –11
Let us consider the first inequality.
11 – 5x > –4
11 – 5x – 11 > –4 – 11
–5x > –15
Divide both the sides by 5 we get,
-5x/5 > -15/5
–x > –3
x < 3
∴ x ∈ (–∞, 3) (1)
Now, let us consider the second inequality.
4x + 13 ≤ –11
4x + 13 – 13 ≤ –11 – 13
4x ≤ –24
Divide both the sides by 4 we get,
4x/4 ≤ –24/4
x ≤ –6
∴ x ∈ (–∞, –6] (2)
From (1) and (2), we get
x ∈ (–∞, 3) ∩ (–∞, –6]
x ∈ (–∞, –6]
∴ The solution of the given system of inequations is (–∞, –6].