Solve each of the following system of inequations in R x – 2 > 0, 3

1.	Solve each of the following system of inequations in R x – 2 > 0, 3x < 18
Answer» Given, x – 2 > 0 and 3x < 18 Let us consider the first inequality. x – 2 < 0 ⇒ x – 2 + 2 < 0 + 2 ⇒ x < 2 ∴ x ∈ ( 2, ∞) ...(1) Now, Let us consider the second inequality. 3x < 18 ⇒ \(\frac{3x}{3}\) < \(\frac{18}{3}\) ⇒ x < 6 ∴ x ∈ (–∞, 6) ....(2) From (1) and (2), we get x ∈ (2, ∞) ∩ (–∞, 6) ∴ x ∈ ( 2, 6) Thus, The solution of the given system of inequations is (2, 6).

Solve each of the following system of inequations in R x – 2 > 0, 3x < 18

Answer»

Given,

x – 2 > 0 and 3x < 18

Let us consider the first inequality.

x – 2 < 0

⇒ x – 2 + 2 < 0 + 2

⇒ x < 2

∴ x ∈ ( 2, ∞) ...(1)

Now,

Let us consider the second inequality.

3x < 18

⇒ \(\frac{3x}{3}\) < \(\frac{18}{3}\)

⇒ x < 6

∴ x ∈ (–∞, 6) ....(2)

From (1) and (2), we get

x ∈ (2, ∞) ∩ (–∞, 6)

∴ x ∈ ( 2, 6)

Thus,

The solution of the given system of inequations is (2, 6).