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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