Question

Solve the system of equations in R.

x – 2 > 0, 3x < 18

Answer 1

Given as

x – 2 > 0 and 3x < 18

Now, let us consider the first inequality.

x – 2 < 0

x – 2 + 2 < 0 + 2

x < 2

∴ x ∈ ( 2, ∞) …(1)

Then, let us consider the second inequality.

3x < 18

Dividing both the sides by 3 we get,

3x/3 < 18/3

x < 6

∴ x ∈ (–∞, 6) …(2)

From (1) and (2), we get

x ∈ (2, ∞) ∩ (–∞, 6)

x ∈ ( 2, 6)

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