Solve each of the following system of inequations in R

x + 3 > 0, 2x < 14

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

⇒ 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).

1