If 3 < a < 7 and 1 < b < 5, find the possible range of a - b.

Question: If 3 < a < 7 and 1 < b < 5, find the possible range of a - b.

Solution:
Given:
3 < a < 7 -------------(1)
1 < b < 5 -------------(2)

Multiply inequality (2) by - 1 to get - b:
1 < b < 5
⇒ - 1 > - b > - 5
⇒ - 5 < - b < - 1 -------------(3)

Add inequality (1) and (3) to find a - b:
3 + (- 5) < a + (- b) < 7 + (- 1)
⇒ - 2 < a - b < 6