Practice Questions →

Chapter 6: Linear Inequalities

NCERT Solutions for CBSE Class 10 Mathematics — 100 solved questions with detailed explanations.

100

Questions

0

Topics

Solved Questions

Q1. The solution of 2x - 3 > 5 is:

x > 4
x > 1
x < 4
x > 8

Difficulty: Easy · Topic: Linear Inequalities

Solution

2x - 3 > 5 ⇒ 2x > 8 ⇒ x > 4.

Q2. 1x + -10 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 0, x > 0.0.

Q3. 1x + -10 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 3, x > 3.0.

Q4. 1x + -10 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 6, x > 6.0.

Q5. 1x + -10 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 9, x > 9.0.

Q6. 1x + -10 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 12, x > 12.0.

Q7. 1x + -10 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 15, x > 15.0.

Q8. 1x + -10 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 18, x > 18.0.

Q9. 1x + -8 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -2, x > -2.0.

Q10. 1x + -8 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 1, x > 1.0.

Q11. 1x + -8 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 4, x > 4.0.

Q12. 1x + -8 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 7, x > 7.0.

Q13. 1x + -8 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 10, x > 10.0.

Q14. 1x + -8 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 13, x > 13.0.

Q15. 1x + -8 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 16, x > 16.0.

Q16. 1x + -6 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -4, x > -4.0.

Q17. 1x + -6 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -1, x > -1.0.

Q18. 1x + -6 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 2, x > 2.0.

Q19. 1x + -6 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 5, x > 5.0.

Q20. 1x + -6 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 8, x > 8.0.

Q21. 1x + -6 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 11, x > 11.0.

Q22. 1x + -6 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 14, x > 14.0.

Q23. 1x + -4 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -6, x > -6.0.

Q24. 1x + -4 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -3, x > -3.0.

Q25. 1x + -4 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 0, x > 0.0.

Q26. 1x + -4 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 3, x > 3.0.

Q27. 1x + -4 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 6, x > 6.0.

Q28. 1x + -4 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 9, x > 9.0.

Q29. 1x + -4 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 12, x > 12.0.

Q30. 1x + -2 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -8, x > -8.0.

Q31. 1x + -2 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -5, x > -5.0.

Q32. 1x + -2 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -2, x > -2.0.

Q33. 1x + -2 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 1, x > 1.0.

Q34. 1x + -2 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 4, x > 4.0.

Q35. 1x + -2 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 7, x > 7.0.

Q36. 1x + -2 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 10, x > 10.0.

Q37. 1x + 0 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -10, x > -10.0.

Q38. 1x + 0 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -7, x > -7.0.

Q39. 1x + 0 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -4, x > -4.0.

Q40. 1x + 0 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -1, x > -1.0.

Q41. 1x + 0 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 2, x > 2.0.

Q42. 1x + 0 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 5, x > 5.0.

Q43. 1x + 0 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 8, x > 8.0.

Q44. 1x + 2 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -12, x > -12.0.

Q45. 1x + 2 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -9, x > -9.0.

Q46. 1x + 2 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -6, x > -6.0.

Q47. 1x + 2 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -3, x > -3.0.

Q48. 1x + 2 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 0, x > 0.0.

Q49. 1x + 2 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 3, x > 3.0.

Q50. 1x + 2 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 6, x > 6.0.

Q51. 1x + 4 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -14, x > -14.0.

Q52. 1x + 4 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -11, x > -11.0.

Q53. 1x + 4 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -8, x > -8.0.

Q54. 1x + 4 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -5, x > -5.0.

Q55. 1x + 4 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -2, x > -2.0.

Q56. 1x + 4 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 1, x > 1.0.

Q57. 1x + 4 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 4, x > 4.0.

Q58. 1x + 6 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -16, x > -16.0.

Q59. 1x + 6 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -13, x > -13.0.

Q60. 1x + 6 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -10, x > -10.0.

Q61. 1x + 6 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -7, x > -7.0.

Q62. 1x + 6 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -4, x > -4.0.

Q63. 1x + 6 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -1, x > -1.0.

Q64. 1x + 6 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 2, x > 2.0.

Q65. 1x + 8 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -18, x > -18.0.

Q66. 1x + 8 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -15, x > -15.0.

Q67. 1x + 8 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -12, x > -12.0.

Q68. 1x + 8 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -9, x > -9.0.

Q69. 1x + 8 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -6, x > -6.0.

Q70. 1x + 8 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -3, x > -3.0.

Q71. 1x + 8 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > 0, x > 0.0.

Q72. 1x + 10 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -20, x > -20.0.

Q73. 1x + 10 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -17, x > -17.0.

Q74. 1x + 10 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -14, x > -14.0.

Q75. 1x + 10 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -11, x > -11.0.

Q76. 1x + 10 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -8, x > -8.0.

Q77. 1x + 10 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -5, x > -5.0.

Q78. 1x + 10 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

1x > -2, x > -2.0.

Q79. 2x + -10 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 0, x > 0.0.

Q80. 2x + -10 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 3, x > 1.5.

Q81. 2x + -10 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 6, x > 3.0.

Q82. 2x + -10 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 9, x > 4.5.

Q83. 2x + -10 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 12, x > 6.0.

Q84. 2x + -10 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 15, x > 7.5.

Q85. 2x + -10 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 18, x > 9.0.

Q86. 2x + -8 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > -2, x > -1.0.

Q87. 2x + -8 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 1, x > 0.5.

Q88. 2x + -8 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 4, x > 2.0.

Q89. 2x + -8 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 7, x > 3.5.

Q90. 2x + -8 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 10, x > 5.0.

Q91. 2x + -8 > 5. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 13, x > 6.5.

Q92. 2x + -8 > 8. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 16, x > 8.0.

Q93. 2x + -6 > -10. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > -4, x > -2.0.

Q94. 2x + -6 > -7. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > -1, x > -0.5.

Q95. 2x + -6 > -4. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 2, x > 1.0.

Q96. 2x + -6 > -1. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 5, x > 2.5.

Q97. 2x + -6 > 2. Solution: x >

Difficulty: Easy · Topic: Inequalities

Solution

2x > 8, x > 4.0.

Q98. The solution set of |x - 2| < 3 is:

(-1, 5)
(2, 5)
(-3, 3)
(-∞, -1) ∪ (5, ∞)

Difficulty: Easy-Medium · Topic: Absolute Inequalities

Solution

|x-2| < 3 ⇒ -3 < x-2 < 3 ⇒ -1 < x < 5. Solution: (-1, 5).

Q99. The solution of |x| < a (a>0) is

(-∞,-a)∪(a,∞)
(0,a)
[-a,a]
(-a, a)

Difficulty: Easy-Medium · Topic: Linear Inequalities

Solution

(-a, a).

Q100. The solution of |x| > a (a>0) is

(-a,a)
(-∞,-a)
(-∞,-a)∪(a,∞)
[a,∞)

Difficulty: Easy-Medium · Topic: Linear Inequalities

Solution

(-∞,-a)∪(a,∞).

Other Chapters in Mathematics

Ch 1: Sets Ch 2: Relations & Functions Ch 3: Trigonometric Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 7: Permutations & Combinations Ch 8: Binomial Theorem Ch 9: Sequences & Series Ch 10: Straight Lines Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 15: Statistics Ch 16: Probability

Want to practice these questions interactively?

Get instant feedback, track progress, and improve with adaptive practice.

Start Practicing Free →