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**Exercise 6.1 : ** Solutions of Questions on Page Number : **122**

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**Exercise 6.2 : ** Solutions of Questions on Page Number : **127**

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**Exercise 6.3 : ** Solutions of Questions on Page Number : **129**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **132**

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**Popular Articles**

Q1 :
**
**

Solve 24*x* < 100, when (i) *x* is a natural number
(ii) *x* is an integer

**Answer :**

The given inequality is 24*x* < 100.

(i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than.

Thus, when *x* is a natural number, the solutions of the
given inequality are 1, 2, 3, and 4.

Hence, in this case, the solution set is {1, 2, 3, 4}.

(ii) The integers less than are …â€“3, â€“2, â€“1, 0, 1, 2, 3, 4.

Thus, when *x* is an integer, the solutions of the given
inequality are

…â€“3, â€“2, â€“1, 0, 1, 2, 3, 4.

Hence, in this case, the solution set is {…â€“3, â€“2, â€“1, 0, 1, 2, 3, 4}.

Answer needs Correction? Click Here

Q2 :
**
**

Solve
-12*x*> 30,
when

(i) *x*is a natural number
(ii) *x*is an integer

**Answer :**

The given inequality is
â€“12*x*>
30.

(i) There is no natural number less than.

Thus, when *x*is a natural
number, there is no solution of the given inequality.

(ii) The integers less than are …, â€“5, â€“4, â€“3.

Thus, when *x*is an integer,
the solutions of the given inequality are

…, â€“5, â€“4, â€“3.

Hence, in this case, the solution set is {…, â€“5, â€“4, â€“3}.

Answer needs Correction? Click Here

Q3 :
**
**

Solve
5*x*- 3 < 7,
when

(i) *x*is an integer
(ii) *x*is a real number

**Answer :**

Q4 :
**
**

Solve 3*x*+ 8 > 2,
when

(i) *x*is an integer
(ii) *x*is a real number

**Answer :**

Q5 :
**
**

Solve the given inequality for real *x*:
4*x* + 3 <
5*x* + 7

**Answer :**

Q6 :
**
**

Solve the given inequality for real *x*:
3*x* - 7
> 5*x* -
1

**Answer :**

Q7 :
**
**

Solve the given inequality for real *x*:
3(*x* -
1)
Ã¢”°Â¤
2 (*x* -
3)

**Answer :**

Q8 :
**
**

Solve the given inequality for real *x*:
3(2 -
*x*)
Ã¢”°Â¥
2(1 -
*x*)

**Answer :**

Q9 :
**
**

Solve the given inequality for real *x*:

**Answer :**

Q10 :
**
**

Solve the given inequality for real *x*:

**Answer :**

Q11 :
**
**

Solve the given inequality for real *x*:

**Answer :**

Q12 :
**
**

Solve the given inequality for real *x*:

**Answer :**

Q13 :
**
**

Solve the given inequality for real *x*:
2(2*x* + 3) - 10 < 6 (*x*
- 2)

**Answer :**

Q14 :
**
**

Solve the given inequality for real *x*:
37 -
(3*x* + 5)
Ã¢”°Â¥
9*x* -
8(*x* -
3)

**Answer :**

Q15 :
**
**

Solve the given inequality for real *x*:

**Answer :**

Q16 :
**
**

Solve the given inequality for real *x*:

**Answer :**

Q17 :
**
**

Solve the given inequality and show the graph of the
solution on number line: 3*x*
- 2 < 2*x*
+1

**Answer :**

Q18 :
**
**

Solve the given inequality and show the graph of the
solution on number line:
5*x* -
3
Ã¢”°Â¥
3*x* -
5

**Answer :**

Q19 :
**
**

Solve the given inequality and show the graph of the
solution on number line: 3(1
- *x*) < 2
(*x* + 4)

**Answer :**

Q20 :
**
**

Solve the given inequality and show the graph of the solution on number line:

**Answer :**

Q21 :
**
**

Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

**Answer :**

Q22 :
**
**

To receive Grade 'A' in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade 'A' in the course.

**Answer :**

Q23 :
**
**

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

**Answer :**

Q24 :
**
**

The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

**Answer :**

Q25 :
**
**

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

[Hint: If *x*is the length
of the shortest board, then *x*,
(*x*+ 3) and
2*x*are the lengths of the second
and third piece, respectively. Thus,
*x*= (*x*
+ 3) + 2*x*
Ã¢”°Â¤91
and 2*x*
Ã¢”°Â¥(*x*
+ 3) + 5]

**Answer :**

Q1 :
**
**

Solve the given inequality graphically in two-dimensional plane:
*x* + *y*
< 5

**Answer :**

Q2 :
**
**

Solve the given inequality graphically in two-dimensional plane:
2*x* +
*y*
Ã¢”°Â¥
6

**Answer :**

Q3 :
**
**

Solve the given inequality graphically in two-dimensional plane:
3*x* +
4*y*
Ã¢”°Â¤
12

**Answer :**

Q4 :
**
**

Solve the given inequality graphically in two-dimensional plane:
*y* + 8
Ã¢”°Â¥
2*x*

**Answer :**

Q5 :
**
**

Solve the given inequality graphically in two-dimensional plane:
*x* -
*y*
Ã¢”°Â¤
2

**Answer :**

Q6 :
**
**

Solve the given inequality graphically in two-dimensional plane:
2*x* -
3*y* > 6

**Answer :**

Q7 :
**
**

Solve the given inequality graphically in two-dimensional plane:
-3*x* +
2*y*
Ã¢”°Â¥
-6

**Answer :**

Q8 :
**
**

Solve the given inequality graphically in two-dimensional plane:
3*y* -
5*x* < 30

**Answer :**

Q9 :
**
**

Solve the given inequality graphically in two-dimensional plane:
*y* < -2

**Answer :**

Q10 :
**
**

Solve the given inequality graphically in two-dimensional plane:
*x* > -3

**Answer :**

Q1 :
**
**

Solve the following system of inequalities graphically:
*x*
Ã¢”°Â¥
3, *y*
Ã¢”°Â¥
2

**Answer :**

Q2 :
**
**

Solve the following system of inequalities
graphically: 3*x* +
2*y*
Ã¢”°Â¤
12, *x*
Ã¢”°Â¥
1, *y*
Ã¢”°Â¥
2

**Answer :**

Q3 :
**
**

Solve the following system of inequalities
graphically: 2*x*
+
*y*Ã¢”°Â¥
6, 3*x* +
4*y*
Ã¢”°Â¤
12

**Answer :**

Q4 :
**
**

Solve the following system of inequalities
graphically: *x* +
*y*Ã¢”°Â¥
4, 2*x*
- *y*
> 0

**Answer :**

Q5 :
**
**

Solve the following system of inequalities
graphically: 2*x*
- *y*
> 1, *x*
- 2*y*
< -1

**Answer :**

Q6 :
**
**

Solve the following system of inequalities
graphically: *x* +
*y*
Ã¢”°Â¤
6, *x* +
*y*
Ã¢”°Â¥
4

**Answer :**

Q7 :
**
**

Solve the following system of inequalities
graphically: 2*x*
+
*y*Ã¢”°Â¥
8, *x* +
2*y*
Ã¢”°Â¥
10

**Answer :**

Q8 :
**
**

Solve the following system of inequalities graphically:
*x* + *y*
Ã¢”°Â¤
9, *y* >
*x*, *x*
Ã¢”°Â¥
0

**Answer :**

Q9 :
**
**

Solve the following system of inequalities graphically:
5*x* +
4*y*
Ã¢”°Â¤
20, *x*
Ã¢”°Â¥
1, *y*
Ã¢”°Â¥
2

**Answer :**

Q10 :
**
**

Solve the following system of inequalities graphically:
3*x* +
4*y*
Ã¢”°Â¤
60, *x* +
3*y*
Ã¢”°Â¤
30, *x*
Ã¢”°Â¥
0, *y*
Ã¢”°Â¥
0

**Answer :**

Q11 :
**
**

Solve the following system of inequalities graphically:
2*x* +
*y*Ã¢”°Â¥
4, *x* +
*y*
Ã¢”°Â¤
3, 2*x* -
3*y*
Ã¢”°Â¤
6

**Answer :**

Q12 :
**
**

Solve the following system of inequalities graphically:

*x* - 2*y*
≤ 3, 3*x* +
4*y* Ã¢â€°Â¥ 12,
*x* Ã¢â€°Â¥ 0,
*y* Ã¢â€°Â¥ 1

**Answer :**

Q13 :
**
**

**[[Q]]**

Solve the following system of inequalities graphically:

4*x* + 3*y*
≤ 60, *y*
Ã¢â€°Â¥ 2*x*, *x*
Ã¢â€°Â¥ 3, *x*,
*y* Ã¢â€°Â¥ 0

**Answer :**

Q14 :
**
**

Solve the following system of inequalities graphically:
3*x* +
2*y*
Ã¢”°Â¤
150, *x* +
4*y*
Ã¢”°Â¤
80, *x*
Ã¢”°Â¤
15, *y*
Ã¢”°Â¥
0, *x*
Ã¢”°Â¥
0

**Answer :**

Q15 :
**
**

Solve the following system of inequalities graphically:
*x* + 2*y*
Ã¢”°Â¤
10, *x* +
*y*
Ã¢”°Â¥
1, *x*
- *y*
Ã¢”°Â¤
0, *x*
Ã¢”°Â¥
0, y
Ã¢”°Â¥
0

**Answer :**

Q1 :
**
**

Solve the inequality 2
Ã¢”°Â¤
3*x* -
4
Ã¢”°Â¤
5

**Answer :**

Q2 :
**
**

Solve the inequality 6
Ã¢”°Â¤
-3(2*x*
- 4) < 12

**Answer :**

Q3 :
**
**

Solve the inequality

**Answer :**

Q4 :
**
**

Solve the inequality

**Answer :**

Q5 :
**
**

Solve the inequality

**Answer :**

Q6 :
**
**

Solve the inequality

**Answer :**

Q7 :
**
**

Solve the inequalities and represent the solution
graphically on number line: 5*x* +
1 > -24, 5*x*
- 1 < 24

**Answer :**

Q8 :
**
**

Solve the inequalities and represent the solution
graphically on number line:
2(*x* -
1) < *x* + 5,
3(*x* + 2) > 2
- *x*

**Answer :**

Q9 :
**
**

Solve the following inequalities and represent the solution graphically on number line:

3*x* - 7 > 2(*x*
- 6), 6 - *x* >
11 - 2*x*

**Answer :**

Q10 :
**
**

Solve the inequalities and represent the solution
graphically on number line:
5(2*x* -
7) - 3(2*x* +
3)
Ã¢”°Â¤
0, 2*x* + 19
Ã¢”°Â¤
6*x* + 47

**Answer :**

Q11 :
**
**

A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by

**Answer :**

Q12 :
**
**

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

**Answer :**

Q13 :
**
**

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

**Answer :**

Q14 :
**
**

IQ of a person is given by the formula

Where MA is mental age and CA is chronological age. If 80 ≤IQ ≤140 for a group of 12 years old children, find the range of their mental age.

**Answer :**

Maths - Maths : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Linear Inequalities ** ( Exercise 6.1, 6.2, 6.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Maths : Chapter 3 - Trigonometric Functions Class 11
- Maths : Chapter 4 - Principle of Mathematical Induction Class 11
- Maths : Chapter 5 - Complex Numbers and Quadratic Equations Class 11
- Maths : Chapter 2 - Relations and Functions Class 11
- Maths : Chapter 1 - Sets Class 11
- Maths : Chapter 9 - Sequences and Series Class 11
- Maths : Chapter 7 - Permutations and Combinations Class 11
- Maths : Chapter 13 - Limits and Derivatives Class 11
- Maths : Chapter 8 - Binomial Theorem Class 11

Exercise 6.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Exercise 6.3 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Question 13 |

Question 14 |

Question 15 |

Exercise Miscellaneous |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Question 13 |

Question 14 |