Solve the system of equations in R.3x – 6 > 0, 2x – 5 > 0

1.	Solve the system of equations in R.3x – 6 > 0, 2x – 5 > 0
Answer» Given as 3x – 6 > 0 and 2x – 5 > 0 Now, let us consider the first inequality. 3x – 6 > 0 3x – 6 + 6 > 0 + 6 3x > 6 Dividing both the sides by 3 we get, 3x/3 > 6/3 x > 2 ∴ x ∈ ( 2, ∞)… (1) Then, let us consider the second inequality. 2x – 5 > 0 2x – 5 + 5 > 0 + 5 2x > 5 Dividing both the sides by 2 we get, 2x/2 > 5/2 x > 5/2 ∴ x ∈ (5/2, ∞)… (2) From (1) and (2), we get x ∈ (2, ∞) ∩ (5/2, ∞) x ∈ (5/2, ∞) Thus, the solution of the given system of inequations is (5/2, ∞).

Answer»

Given as

3x – 6 > 0 and 2x – 5 > 0

Now, let us consider the first inequality.

3x – 6 > 0

3x – 6 + 6 > 0 + 6

3x > 6

Dividing both the sides by 3 we get,

3x/3 > 6/3

x > 2

∴ x ∈ ( 2, ∞)… (1)

Then, let us consider the second inequality.

2x – 5 > 0

2x – 5 + 5 > 0 + 5

2x > 5

Dividing both the sides by 2 we get,

2x/2 > 5/2

x > 5/2

∴ x ∈ (5/2, ∞)… (2)

From (1) and (2), we get

x ∈ (2, ∞) ∩ (5/2, ∞)

x ∈ (5/2, ∞)

Thus, the solution of the given system of inequations is (5/2, ∞).

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