Typical numericals on Linear Inequality for JEE and CBSE board exams:

1. Solve the inequality: 2x + 5 < 15. Solution: 2x < 10 Therefore, x < 5.

2. Find the solution set of the inequality: -3x + 4 > -5. Solution: -3x > -9 Therefore, x < 3.

3. Solve the inequality: 4 - 2x ≥ 6. Solution: -2x ≥ 2 Therefore, x ≤ -1.

4. Find the interval of values of x for which the inequality 3x - 5 < 10 - 2x holds true. Solution: 3x - 5 < 10 - 2x 5x < 15 Therefore, x < 3.

5. Determine the range of values of x for which the inequality 2x + 3 ≤ 5x - 2 is satisfied. Solution: 2x + 3 ≤ 5x - 2 3x ≤ -5 Therefore, x ≤ -5/3.

6. Solve the inequality: 2(3x - 4) > 5(2x + 1) - 3. Solution: 6x - 8 > 10x + 5 - 3 6x - 8 > 10x - 2 10x - 6x > 2+8 4x > 10 Therefore, x > 5/2.

7. Find the solution set of the inequality: 4 - 3(2x + 5) ≥ 7 - 2(3x - 4). Solution: 4 - 6x - 15 ≥ 7 - 6x + 8 -11 - 6x ≥ 15 - 6x -11 ≥ 15 Therefore, no real solution exists.

8. Determine the range of values of x for which the inequality (x + 2)/(x - 1) < 2 is true. Solution: (x + 2)/(x - 1) < 2 x + 2 < 2(x - 1) x + 2 < 2x - 2 x - 2x < -2 -2 -x < -4 Therefore, x > 4.

9. Solve the inequality: 1/3(x - 2) > 1/2(x + 1) + 5. Solution: 1/3(x - 2) > 1/2(x + 1) + 5 x - 2 > 3/2(x + 1) + 15 x - 2 > 3/2x + 3/2 + 15 2(x - 2) > 3(3/2x + 3/2 + 15) 2x - 4 > 9/2x + 9/2 + 45 2x - 9/2x > 9/2 + 45 + 4 5/2x > 59/2 Therefore, x > 59/5.

10. Find the solution set of the inequality: (2x - 3)/(4 - x) ≥ 1. Solution: (2x - 3)/(4 - x) ≥ 1 (2x - 3) ≥ 1(4 - x) 2x - 3 ≥ 4 - x 2x + x ≥ 4 + 3 3x ≥ 7 Therefore, x ≥ 7/3.