Solve each of the following system of inequations in R 2x – 3 < 7,

1.	Solve each of the following system of inequations in R 2x – 3 < 7, 2x > –4
Answer» Given, 2x – 3 < 7 and 2x > –4 Let us consider the first inequality. 2x – 3 < 7 ⇒ 2x – 3 + 3 < 7 + 3 ⇒ 2x < 10 ⇒ \(\frac{2x}{2}\) < \(\frac{10}{2}\) ⇒ x < 5 ∴ x ∈ ( –∞, 5) ...(1) Now, Let us consider the second inequality. 2x > –4 ⇒ \(\frac{2x}{2}\) > \(\frac{-4}{2}\) ⇒ x > –2 ∴ x ∈ (–2, ∞) ...(2) From (1) and (2), we get x ∈ (–∞, 5) ∩ (–2, ∞) ∴ x ∈ (–2, 5) Thus, The solution of the given system of inequations is (–2, 5).

Solve each of the following system of inequations in R 2x – 3 < 7, 2x > –4

Answer»

Given,

2x – 3 < 7 and 2x > –4

Let us consider the first inequality.

2x – 3 < 7

⇒ 2x – 3 + 3 < 7 + 3

⇒ 2x < 10

⇒ \(\frac{2x}{2}\) < \(\frac{10}{2}\)

⇒ x < 5

∴ x ∈ ( –∞, 5) ...(1)

Now,

Let us consider the second inequality.

2x > –4

⇒ \(\frac{2x}{2}\) > \(\frac{-4}{2}\)

⇒ x > –2

∴ x ∈ (–2, ∞) ...(2)

From (1) and (2), we get

x ∈ (–∞, 5) ∩ (–2, ∞)

∴ x ∈ (–2, 5)

Thus,

The solution of the given system of inequations is (–2, 5).