Question

If x ∈ I, A is the solution set of 2 (x – 1) < 3 x – 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩ B.

Answer 1

2 (x – 1) < 3 x – 1
2x – 2 < 3x – 1
2x – 3x < – 1 + 2
⇒ – x < 1 x > – 1
Solution set A = {0, 1, 2, 3, ...}
4x – 3 ≤ 8 + x
4x – x ≤ 8 + 3
⇒ 3x ≤ 11

⇒ x ≤ `(11)/(3)`
Solution set B = {3, 2, 1, 0, – 1…}
A ∩ B = {0, 1, 2, 3}.