Question -
Answer -
Given:
2x + 5 ≤ 0 and x – 3 ≤ 0
Let us consider the first inequality.
2x + 5 ≤ 0
2x + 5 – 5 ≤ 0 – 5
2x ≤ –5
Divide both the sides by 2 we get,
2x/2 ≤ –5/2
x ≤ – 5/2
∴ x ∈ (–∞, -5/2]… (1)
Now, let us consider the second inequality.
x – 3 ≤ 0
x – 3 + 3 ≤ 0 + 3
x ≤ 3
∴ x ∈ (–∞, 3]… (2)
From (1) and (2), we get
x ∈ (–∞, -5/2] ∩ (–∞, 3)
x ∈ (–∞, -5/2]
∴ The solution of the given system of inequations is (–∞, -5/2].