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