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

1.	Solve each of the following system of inequations in R x + 3 > 0, 2x < 14
Answer» Given, x + 3 < 0 and 2x < 14 Let us consider the first inequality. x + 3 < 0 ⇒ x + 3 – 3 < 0 – 3 ⇒ x < –3 ∴ x ∈ ( –∞, –3) ...(1) Now, Let us consider the second inequality. 2x < 14 ⇒ \(\frac{2x}{2}\) < \(\frac{14}{2}\) ⇒ x < 7 ∴ x ∈ (–∞, 7) ...(2) From (1) and (2), we get x ∈ (–∞, –3) ∩ (–∞, 7) ∴ x ∈ ( –∞, –3) Thus, The solution of the given system of inequations is (–∞, –3).

Solve each of the following system of inequations in R x + 3 > 0, 2x < 14

Answer»

Given,

x + 3 < 0 and 2x < 14

Let us consider the first inequality.

x + 3 < 0

⇒ x + 3 – 3 < 0 – 3

⇒ x < –3

∴ x ∈ ( –∞, –3) ...(1)

Now,

Let us consider the second inequality.

2x < 14

⇒ \(\frac{2x}{2}\) < \(\frac{14}{2}\)

⇒ x < 7

∴ x ∈ (–∞, 7) ...(2)

From (1) and (2), we get

x ∈ (–∞, –3) ∩ (–∞, 7)

∴ x ∈ ( –∞, –3)

Thus,

The solution of the given system of inequations is (–∞, –3).