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# Frank solutions for Class 10 Maths chapter 5 - Linear Inequations

## Chapter 5: Linear Inequations

Exercise 5.1

#### Frank solutions for Class 10 Maths Chapter 5 Exercise Exercise 5.1 [Pages 74 - 75]

Exercise 5.1 | Q 1.1 | Page 74

Solve for x in the following in equation, if the replacement set is N<10:

x + 5 > 11

Exercise 5.1 | Q 1.2 | Page 74

Solve for x in the following in equation, if the replacement set is N<10:

2x + 1 < 17

Exercise 5.1 | Q 1.3 | Page 74

Solve for x in the following in equation, if the replacement set is N<10:

3x - 5 < 7

Exercise 5.1 | Q 1.4 | Page 74

Solve for x in the following in equation, if the replacement set is N<10:

8 - 3x > 2

Exercise 5.1 | Q 1.5 | Page 74

Solve for x in the following in equation, if the replacement set is N<10:

5 - 2x < 11

Exercise 5.1 | Q 2.01 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

3x >12

Exercise 5.1 | Q 2.02 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

2x - 3 < 7

Exercise 5.1 | Q 2.03 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

3x + 2 ≤ 11

Exercise 5.1 | Q 2.04 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

14 - 3x > 5

Exercise 5.1 | Q 2.05 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

7x + 11 > 16 - 3x

Exercise 5.1 | Q 2.06 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

3x + 25 < 8x - 10

Exercise 5.1 | Q 2.07 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

2(3x - 5) ≤ 8

Exercise 5.1 | Q 2.08 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

x + 7 ≥ 15 + 3x

Exercise 5.1 | Q 2.09 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

2x - 7 ≥  5x + 8

Exercise 5.1 | Q 2.1 | Page 74

Solve for x in the following in-equation, if the replacement set is R;

9 - 4x ≤ 15 - 7x

Exercise 5.1 | Q 3 | Page 75

Solve for x : 6 - 10x < 36, x ∈  {-3, -2, -1, O, 1, 2}

Exercise 5.1 | Q 4 | Page 75

Solve for x : 3 - 2x ≥ x - 12, x ∈  N

Exercise 5.1 | Q 5 | Page 75

Solve for x: 5x - 9 ≤ 15 - 7x ,  x ∈ W

Exercise 5.1 | Q 6 | Page 75

Solve for x : 7 + 5x > x - 13, where x is a negative integer.

Exercise 5.1 | Q 7 | Page 75

Solve for x : 5x - 14 < 18 - 3x, where x ∈  W

Exercise 5.1 | Q 8 | Page 75

Solve for x : 2x + 7 ≥  5x - 14, where x is a positive prime number.

Exercise 5.1 | Q 9 | Page 75

Solve for x : "x"/4 + 3 <= "x"/3 + 4 , where xis a negative odd number.

Exercise 5.1 | Q 10 | Page 75

Solve for x : ("x" + 3)/3 <= ("x" + 8)/4 , where x is a positive even number.

Exercise 5.1 | Q 11.1 | Page 75

If x + 17 ≤  4x + 9, find the smallest value of x, when:

x ∈  Z

Exercise 5.1 | Q 11.2 | Page 75

If x + 17 ≤  4x + 9, find the smallest value of x, when:

x ∈ R

Exercise 5.1 | Q 12 | Page 75

If (2 "x" + 7)/3 <=  (5 "x" +1)/4 , find the smallest value of x, when:

(i) x ∈ R

(ii) x ∈ Z

Exercise 5.1 | Q 13.01 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

2x - 11≤ 7 - 3x, x ∈ N

Exercise 5.1 | Q 13.02 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

3(5x+ 3) ≥ 2(9x-17), x ∈ W

Exercise 5.1 | Q 13.03 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

2(3x-5) > 5(13-2x), x ∈ W

Exercise 5.1 | Q 13.04 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line :

3x - 9 ≤ 4x - 7 < 2x + 5,  x ∈  R

Exercise 5.1 | Q 13.05 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

2x - 7 < 5x + 2 ≤ 3x + 14, x ∈ R

Exercise 5.1 | Q 13.06 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

-3 <= 1/2 - (2 "x")/3 <= 2 2/3 , x  ∈ N

Exercise 5.1 | Q 13.07 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line :

4 3/4 >= "x" + 5/6 > 1/3 , x ∈ R

Exercise 5.1 | Q 13.08 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line :

1/3 (2x - 1) < 1/4 (x + 5) < 1/6 (3x + 4), x ∈ R

Exercise 5.1 | Q 13.09 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

1/3 (5"x" - 8) >= 1/2 (4"x" - 7) , x ∈ R

Exercise 5.1 | Q 13.1 | Page 75

Solve the following linear in-equation and graph the solution set on a real number line:

5/4 "x" > 1 + 1/3 (4"x" - 1) , x ∈ R

Exercise 5.1 | Q 14.1 | Page 75

If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines :

P ∩ Q

Exercise 5.1 | Q 14.2 | Page 75

If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines:

Q' ∩ P

Exercise 5.1 | Q 14.3 | Page 75

If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines:

P-Q

Exercise 5.1 | Q 15.1 | Page 75

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines:

P ∩ Q

Exercise 5.1 | Q 15.2 | Page 75

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines:

P - Q

Exercise 5.1 | Q 15.3 | Page 75

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines:

P ∩ Q'

Exercise 5.1 | Q 16.1 | Page 75

If P = {x : 7x - 4 > 5x + 2, x ∈  R} and Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}, represent the following solution set on different number lines:

P ∩ Q

Exercise 5.1 | Q 16.2 | Page 75

If P = {x : 7x - 4 > 5x + 2, x ∈  R} and Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}, represent the following solution set on different number lines:

P' ∩ Q

Exercise 5.1

## Frank solutions for Class 10 Mathematics chapter 5 - Linear Inequations

Frank solutions for Class 10 Maths chapter 5 (Linear Inequations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Frank Class 10 Mathematics Part 2 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 5 Linear Inequations are Linear Inequations in One Unknown, Solving Algebraically and Writing the Solution in Set Notation Form, Representation of Solution on the Number Line.

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