**Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9}, find the values of x for which -3 < 2x – 1 < x + 4.**

**Solution:**

-3 < 2x – 1 < x + 4.

⇒ – 3 < 2x – 1 and 2x – 1 < x + 4

⇒ – 2x < – 1 + 3 and 2x – x < 4 + 1

⇒ – 2x < 2 and x < 5

⇒ – x < 1

⇒ x > – 1

– 1 < x < 5

x ∈ {1, 2, 3, 4, 5, 6, 7, 9}

Solution set = {1, 2, 3, 4} Ans.

#### Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N

**Solution:**

1 ≥ 15 – 7x > 2x – 27

1 ≥ 15 – 7x and 15 – 7x > 2x – 27