# Important Questions for Class 11 Chapter 6 - Linear Inequalities

The Important Questions for CBSE class 11th Maths PDF includes complete sets of questions from Maths chapter-wise and topic-wise. It will help you to prepare well for your Class tests, final exams or any other competitive exams.

**Important questions based on NCERT syllabus for Class 11 Chapter 6 - Linear Inequalities:**

*Question 1*: Solve the inequation 1/3(4/5 x + 5)≥ 1/2(x-4)

*Solution*:

2(4/5 x + 5) ≥ 3(x-4)

8/5 x + 10 ≥ 3x - 12

8/5 x + 10 - 10 ≥ 3x - 12 - 10

8/5 x ≥ 3x - 22

8/5 x - 3x ≥ 3x - 3x - 22

-7x/5 ≥ - 22

-7x/5 * 5/7 ≥ - 22 * 5/7

-x ≥ -110/7

x ≤ -110/7

*Question 2*: Solve the system of inequation, x-3<0 and x+5>25

*Solution*:

Given x-3<0

x+5>25

Consider x-3<0

=> x -3+3 < 0+3

=> x<3 ............(1)

Consider x+5>25

x+5-5> 25 - 5

x>20 ..........(2)

From (1) and (2) we can say the x lies between 20 and 3, symbollycally 20<x<3

Hence the solution of the system is 20 < x < 3

*Question 3*: Solve the inequation x/5 ≥ (3x -5)/3 - (2x + 7)/2

*Solution*:

Given x/5 ≥ (3x -5)/3 - (2x + 7)/2

x/5 ≥ (6(3x -5) - 6(2x + 7))/6 [taking LCM of 2 and 3 and solving]

x/5 ≥ (18x - 30 - 12x - 42)/6

x/5 ≥ (6x - 72)/6

x/5 ≥ (6(x - 12))/6

x/5 ≥ (x - 12)

x ≥ 5(x-12)

x ≥ 5x - 60

x - 5x ≥ -60

-4x ≥ -60

-x ≥ -60/4

-x ≥ -15

x ≤ 15