Solve each of the following system of inequations in R 11 – 5x > �

1.	Solve each of the following system of inequations in R 11 – 5x > –4, 4x + 13 ≤ –11
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 ⇒ \(\frac{-5x}{5}\) > \(\frac{-15}{5}\) ⇒ –x > –3 ⇒ x < 3 ∴ x ∈ (–∞, 3) ...(1) Now, Let us consider the second inequality. 4x + 13 ≤ –11 ⇒ 4x + 13 – 13 ≤ –11 – 13 ⇒ 4x ≤ –24 ⇒ \(\frac{4x}{4}\) ≤ \(\frac{-24}{4}\) ⇒ 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].

Solve each of the following system of inequations in R 11 – 5x > –4, 4x + 13 ≤ –11

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

⇒ \(\frac{-5x}{5}\) > \(\frac{-15}{5}\)

⇒ –x > –3

⇒ x < 3

∴ x ∈ (–∞, 3) ...(1)

Now,

Let us consider the second inequality.

4x + 13 ≤ –11

⇒ 4x + 13 – 13 ≤ –11 – 13

⇒ 4x ≤ –24

⇒ \(\frac{4x}{4}\) ≤ \(\frac{-24}{4}\)

⇒ 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].