**1. Solve the inequation, 3x – 11 < 3 where x ∈ {1,2,3,……,10}. Also, represent its solution on a number line.**

**Solution:**

**2. Solve 2(x – 3) < 1,x ∈ {1,2,3,….10}**

**Solution:**

**3. Solve 5 – 4x > 2 – 3x,x ∈ W. Also represent its solution on the number line.**

**Solution:**

**4. List the solution set of 30 – 4 (2x – 1) < 30, given that x is a positive integer.**

**Solution:**

**8. Solve x – 3 (2 + x) > 2 (3x – 1),x ∈ { – 3,– 2,– 1,0,1,2,3}. Also represent its solution on the number line.**

**Solution:**

**9. Given x ∈ {1,2,3,4,5,6,7,9} solve x – 3 < 2x – 1.**

**Solution:**

**10. Given A = {x: x ∈ I,– 4 ≤ x ≤ 4}, solve 2x – 3 < 3 where x has the domain A. Graph the solution set on the number line.**

**Solution:**

**Solution:**

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

**Solution:**

**18. Solve: 1 ≥ 15 – 7x > 2x – 27,x ∈ N**

**Solution:**

**19. If x ∈ Z,solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.**

**Solution:**

**23. Solve the inequation – 3 ≤ 3 – 2x < 9,x ∈ R. Represent your solution on a number line.**

**Solution:**

**24. Solve 2 ≤ 2x – 3 ≤ 5,x ∈ R and mark it on a number line.**

**Solution:**

**25. Given that x ∈ R, solve the following inequation and graph the solution on the number line: -1 ≤ 3 + 4x < 23.**

**Solution:**

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

**Solution:**

**33. If P is the solution set of -3x + 4 < 2x – 3,x ∈ N and Q is the solution set of 4x – 5 < 12,x ∈ W, find**

**(i) P ∩ Q**

**(ii) Q – P.**

**(ii) Q – P.**

**Solution:**

**35. Given: P {x∶ 5 < 2x – 1 ≤ 11,x ∈ R}**

**Q {x∶ – 1 ≤ 3 + 4x < 23,x ∈ I} where**

**R = (real numbers), I = (integers)**

**Represent P and Q on number line. Write down the elements of P ∩ Q.**

**Solution:**

**37. Given 20 – 5 x < 5 (x + 8), find the smallest value of x, when**

**(i) x ∈ I**

**(ii) x ∈ W**

**(iii) x ∈ N.**

**Solution:**

**39. Solve the given inequation and graph the solution on the number line:**

**2y – 3 < y + 1 ≤ 4y + 7;y ∈ R.**

**Solution:**

**41. Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.**

**Solution**:

**42. One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.**

**Solution:**

**CHAPTER TEST**

**1. Solve the inequation: 5x – 2 ≤ 3 (3 – x) where x ∈ {-2, -1, 0, 1, 2, 3, 4}. Also represent its solution on the number line.**

**Solution:**

**2. Solve the inequation: 6x – 5 < 3x + 4,x ∈ I**

**Solution:**

**3. Find the solution set of the inequation x + 5 ≤ 2x + 3; x ∈ R**

**Graph the solution set on the number line.**

**Solution:**

**4. If x ∈ R (real numbers) and -1 < 3 – 2x ≤ 7, find solution set and present it on a number line.**

**Solution:**