Solve each of the following system of inequations in R 5x – 1 < 24,

1.	Solve each of the following system of inequations in R 5x – 1 < 24, 5x + 1 > –24
Answer» Given, 5x – 1 < 24 and 5x + 1 > –24 Let us consider the first inequality. 5x – 1 < 24 ⇒ 5x – 1 + 1 < 24 + 1 ⇒ 5x < 25 ⇒ \(\frac{5x}{5}\) < \(\frac{25}{5}\) ⇒ x < 5 ∴ x ∈ (–∞, 5) ...(1) Now, Let us consider the second inequality. 5x + 1 > –24 ⇒ 5x + 1 – 1 > –24 – 1 ⇒ 5x > –25 ⇒ \(\frac{5x}{5}\) > \(\frac{-25}{5}\) ⇒ x > –5 ∴ x ∈ (–5, ∞) (2) From (1) and (2), we get x ∈ (–∞, 5) ∩ (–5, ∞) ∴ x ∈ (–5, 5) Thus, The solution of the given system of inequations is (–5, 5).

Solve each of the following system of inequations in R 5x – 1 < 24, 5x + 1 > –24

Answer»

Given,

5x – 1 < 24 and 5x + 1 > –24

Let us consider the first inequality.

5x – 1 < 24

⇒ 5x – 1 + 1 < 24 + 1

⇒ 5x < 25

⇒ \(\frac{5x}{5}\) < \(\frac{25}{5}\)

⇒ x < 5

∴ x ∈ (–∞, 5) ...(1)

Now,

Let us consider the second inequality.

5x + 1 > –24

⇒ 5x + 1 – 1 > –24 – 1

⇒ 5x > –25

⇒ \(\frac{5x}{5}\) > \(\frac{-25}{5}\)

⇒ x > –5

∴ x ∈ (–5, ∞) (2)

From (1) and (2), we get

x ∈ (–∞, 5) ∩ (–5, ∞)

∴ x ∈ (–5, 5)

Thus,

The solution of the given system of inequations is (–5, 5).