Solve the system of equations in R.2x + 6 ≥ 0, 4x – 7 < 0

1.	Solve the system of equations in R.2x + 6 ≥ 0, 4x – 7 < 0
Answer» Given as 2x + 6 ≥ 0 and 4x – 7 < 0 Now, let us consider the first inequality. 2x + 6 ≥ 0 2x + 6 – 6 ≥ 0 – 6 2x ≥ –6 Dividing both the sides by 2 we get, 2x/2 ≥ -6/2 x ≥ -3 ∴ x ∈ [–3, ∞) …(1) Then, let us consider the second inequality. 4x – 7 < 0 4x – 7 + 7 < 0 + 7 4x < 7 Dividing both the sides by 4 we get, 4x/4 < 7/4 x < 7/4 ∴ x ∈ [–∞, 7/4) …(2) From (1) and (2), we get x ∈ (-3, ∞) ∩ (–∞, 7/4) x ∈ (-3, 7/4) ∴ The solution of the given system of inequations is (-3, 7/4).

Answer»

Given as

2x + 6 ≥ 0 and 4x – 7 < 0

Now, let us consider the first inequality.

2x + 6 ≥ 0

2x + 6 – 6 ≥ 0 – 6

2x ≥ –6

Dividing both the sides by 2 we get,

2x/2 ≥ -6/2

x ≥ -3

∴ x ∈ [–3, ∞) …(1)

Then, let us consider the second inequality.

4x – 7 < 0

4x – 7 + 7 < 0 + 7

4x < 7

Dividing both the sides by 4 we get,

4x/4 < 7/4

x < 7/4

∴ x ∈ [–∞, 7/4) …(2)

From (1) and (2), we get

x ∈ (-3, ∞) ∩ (–∞, 7/4)

x ∈ (-3, 7/4)

∴ The solution of the given system of inequations is (-3, 7/4).

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