Question

Solve each of the following system of equations in R.

2x − 7 > 5 − x, 11 − 5x ≤ 1

Answer 1

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, ∞).