Solve the system of equations in R.2x – 3 < 7, 2x > –4

Solve the system of equations in R.2x – 3 –4

FullFormDefinition · 2025-09-29T19:57:50.000000Z

Solve the system of equations in R.2x – 3 –4

1.	Solve the system of equations in R.2x – 3 < 7, 2x > –4
Answer» Given as 2x – 3 < 7 and 2x > –4 Now, let us consider the first inequality. 2x – 3 < 7 2x – 3 + 3 < 7 + 3 2x < 10 Dividing both the sides by 2 we get, 2x/2 < 10/2 x < 5 ∴ x ∈ ( –∞, 5)… (1) Then, let us consider the second inequality. 2x > –4 Dividing both the sides by 2 we get, 2x/2 > -4/2 x > –2 ∴ x ∈ (–2, ∞)… (2) From (1) and (2), we get x ∈ (–∞, 5) ∩ (–2, ∞) x ∈ (–2, 5) Thus, the solution of the given system of inequations is (–2, 5).

Answer»

Given as

2x – 3 < 7 and 2x > –4

Now, let us consider the first inequality.

2x – 3 < 7

2x – 3 + 3 < 7 + 3

2x < 10

Dividing both the sides by 2 we get,

2x/2 < 10/2

x < 5

∴ x ∈ ( –∞, 5)… (1)

Then, let us consider the second inequality.

2x > –4

Dividing both the sides by 2 we get,

2x/2 > -4/2

x > –2

∴ x ∈ (–2, ∞)… (2)

From (1) and (2), we get

x ∈ (–∞, 5) ∩ (–2, ∞)

x ∈ (–2, 5)

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