Solve each of the following system of inequations in R

2x – 3 < 7, 2x > –4

Given 2x – 3 < 7 and 2x > –4

Let us consider the first inequality.

2x – 3 < 7

⇒ 2x – 3 + 3 < 7 + 3

⇒ 2x < 10

⇒ x < 5

∴ x ∈ ( –∞, 5) (1)

Now, let us consider the second inequality.

2x > –4

⇒ 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).

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