Solve each of the following system of inequations in R

11 – 5x > –4, 4x + 13 ≤ –11

Given 11 – 5x > –4 and 4x + 13 ≤ –11

Let us consider the first inequality.

11 – 5x > –4

⇒ 11 – 5x – 11 > –4 – 11

⇒ –5x > –15

⇒ –x > –3

⇒ x < 3

∴ x ∈ (–∞, 3) (1)

Now, let us consider the second inequality.

4x + 13 ≤ –11

⇒ 4x + 13 – 13 ≤ –11 – 13

⇒ 4x ≤ –24

⇒ x ≤ –6

∴ x ∈ (–∞, –6] (2)

From (1) and (2), we get

x ∈ (–∞, 3) ∩ (–∞, –6]

∴ x ∈ (–∞, –6]

Thus, the solution of the given system of inequations is (–∞, –6].

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