Solve each of the following system of inequations in R
2x + 5 ≤ 0, x – 3 ≤ 0
Given 2x + 5 ≤ 0 and x – 3 ≤ 0
Let us consider the first inequality.
2x + 5 ≤ 0
⇒ 2x + 5 – 5 ≤ 0 – 5
⇒ 2x ≤ –5
(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
Thus, the solution of the given system of inequations is 
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