Solve the system of equations in R.2x – 7 > 5 – x, 11 – 5x ≤

1.	Solve the system of equations in R.2x – 7 > 5 – x, 11 – 5x ≤ 1
Answer» Given as 2x – 7 > 5 – x and 11 – 5x ≤ 1 Now, let us consider the first inequality. 2x – 7 > 5 – x 2x – 7 + 7 > 5 – x + 7 2x > 12 – x 2x + x > 12 – x + x 3x > 12 Dividing both the sides by 3 we get, 3x/3 > 12/3 x > 4 ∴ x ∈ (4, ∞) … (1) Then, let us consider the second inequality. 11 – 5x ≤ 1 11 – 5x – 11 ≤ 1 – 11 –5x ≤ –10 Dividing both the sides by 5 we get, -5x/5 ≤ -10/5 –x ≤ –2 x ≥ 2 ∴ x ∈ (2, ∞) … (2) From (1) and (2) we get x ∈ (4, ∞) ∩ (2, ∞) x ∈ (4, ∞) Hence, the solution of the given system of inequations is (4, ∞).

Solve the system of equations in R.2x – 7 > 5 – x, 11 – 5x ≤ 1

Answer»

Given as

2x – 7 > 5 – x and 11 – 5x ≤ 1

Now, let us consider the first inequality.

2x – 7 > 5 – x

2x – 7 + 7 > 5 – x + 7

2x > 12 – x

2x + x > 12 – x + x

3x > 12

Dividing both the sides by 3 we get,

3x/3 > 12/3

x > 4
∴ x ∈ (4, ∞) … (1)

Then, let us consider the second inequality.

11 – 5x ≤ 1

11 – 5x – 11 ≤ 1 – 11

–5x ≤ –10

Dividing both the sides by 5 we get,

-5x/5 ≤ -10/5

–x ≤ –2

x ≥ 2

∴ x ∈ (2, ∞) … (2)

From (1) and (2) we get

x ∈ (4, ∞) ∩ (2, ∞)

x ∈ (4, ∞)

Hence, the solution of the given system of inequations is (4, ∞).