Solve the system of equations in R.x – 2 > 0, 3x < 18

1.	Solve the system of equations in R.x – 2 > 0, 3x < 18
Answer» 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).

Answer»

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).

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