Solve the system of equations in R.3x – 1 ≥ 5, x + 2 > -1

1.	Solve the system of equations in R.3x – 1 ≥ 5, x + 2 > -1
Answer» Given as 3x – 1 ≥ 5 and x + 2 > –1 Now, let us consider the first inequality. 3x – 1 ≥ 5 3x – 1 + 1 ≥ 5 + 1 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. x + 2 > –1 x + 2 – 2 > –1 – 2 x > –3 ∴ x ∈ (–3, ∞)… (2) From (1) and (2), we get x ∈ (2, ∞) ∩ (–3, ∞) x ∈ (2, ∞) Hence, the solution of the given system of inequations is (2, ∞).

Answer»

Given as

3x – 1 ≥ 5 and x + 2 > –1

Now, let us consider the first inequality.

3x – 1 ≥ 5

3x – 1 + 1 ≥ 5 + 1

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.

x + 2 > –1

x + 2 – 2 > –1 – 2

x > –3

∴ x ∈ (–3, ∞)… (2)

From (1) and (2), we get

x ∈ (2, ∞) ∩ (–3, ∞)

x ∈ (2, ∞)

Hence, the solution of the given system of inequations is (2, ∞).

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