#### Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line. (2011)

**Solution:**

2x – 5 ≤ 5x + 4 < 11 2x – 5 ≤ 5x + 4

⇒ 2x – 5 – 4 ≤ 5x and 5x + 4 < 11

⇒ 2x – 9 ≤ 5x and 5x < 11 – 4

and 5x < 7

⇒ 2x – 5x ≤ 9 and x <

⇒ 3x > – 9 and x< 1.4

⇒ x > – 3

#### 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.

**Solution:**

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 ≤

Solution set B = {3, 2, 1, 0, – 1…}

A ∩ B = {0, 1, 2, 3} Ans.