Solve each of the following system of inequations in R 3x – 1 ≥ 5

1.	Solve each of the following system of inequations in R 3x – 1 ≥ 5, x + 2 > –1
Answer» Given, 3x – 1 ≥ 5 and x + 2 > –1 Let us consider the first inequality. 3x – 1 ≥ 5 ⇒ 3x – 1 + 1 ≥ 5 + 1 ⇒ 3x ≥ 6 ⇒ \(\frac{3x}{3}\) ≥ \(\frac{6}{3}\) ⇒ x ≥ 2 ∴ x ∈ (2, ∞) ...(1) Now, Let us consider the second inequality. x + 2 > –1 ⇒ x + 2 – 2 > –1 – 2 ⇒ x > –3 ∴ x ∈ (–3, ∞) ...(2) From (1) and (2), we get x ∈ (2, ∞) ∩ (–3, ∞) ∴ x ∈ (2, ∞) Thus, The solution of the given system of inequations is (2, ∞).

Solve each of the following system of inequations in R 3x – 1 ≥ 5, x + 2 > –1

Answer»

Given,

3x – 1 ≥ 5 and x + 2 > –1

Let us consider the first inequality.

3x – 1 ≥ 5

⇒ 3x – 1 + 1 ≥ 5 + 1

⇒ 3x ≥ 6

⇒ \(\frac{3x}{3}\) ≥ \(\frac{6}{3}\)

⇒ x ≥ 2

∴ x ∈ (2, ∞) ...(1)

Now,

Let us consider the second inequality.

x + 2 > –1

⇒ x + 2 – 2 > –1 – 2

⇒ x > –3

∴ x ∈ (–3, ∞) ...(2)

From (1) and (2), we get

x ∈ (2, ∞) ∩ (–3, ∞)

∴ x ∈ (2, ∞)

Thus,

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