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, ∞).
