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NCERT Class 11 - Math

Parvin Sinclair, G.P. Dikshit

Chapter 6

Linear Inequalities - all with Video Answers

Educators


Section 1

Introduction

03:47

Problem 1

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

Brock Benorden
Brock Benorden
Numerade Educator
00:46

Problem 2

Solve $-12 x>30$, when
(i) $x$ is a natural number.
(ii) $x$ is an integer.

James Kiss
James Kiss
Numerade Educator
01:29

Problem 3

Solve $5 x-3<7$, when
(i) $x$ is an integer.
(ii) $x$ is a real number.

Edward Downes
Edward Downes
Numerade Educator
05:08

Problem 4

Solve $3 x+8>2$, when
(i) $x$ is an integer.
(ii) $x$ is a real number.

AG
Ankit Gupta
Numerade Educator
00:33

Problem 5

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
4 x+3<5 x+7
$$

Julie Silva
Julie Silva
Numerade Educator
01:10

Problem 6

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
3 x-7>5 x-1
$$

Julie Silva
Julie Silva
Numerade Educator
00:49

Problem 7

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
3(x-1) \leq 2(x-3)
$$

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:55

Problem 8

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
3(2-x) \geq 2(1-x)
$$

Nick Johnson
Nick Johnson
Numerade Educator
02:13

Problem 9

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
x+\frac{x}{2}+\frac{x}{3}<11
$$

AG
Ankit Gupta
Numerade Educator
02:15

Problem 10

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
\frac{x}{3}>\frac{x}{2}+1
$$

AG
Ankit Gupta
Numerade Educator
01:22

Problem 11

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}
$$

Joshua Hale
Joshua Hale
Numerade Educator
04:05

Problem 12

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
\frac{1}{2}\left(\frac{3 x}{5}+4\right) \geq \frac{1}{3}(x-6)
$$

Nick Johnson
Nick Johnson
Numerade Educator
01:25

Problem 13

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
2(2 x+3)-10<6(x-2)
$$

Joshua Hale
Joshua Hale
Numerade Educator
01:38

Problem 14

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
37-(3 x+5) \geq 9 x-8(x-3)
$$

Derrick Hanson
Derrick Hanson
Numerade Educator
01:10

Problem 15

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}
$$

Julie Silva
Julie Silva
Numerade Educator
01:22

Problem 16

Solve the inequalities in Exercises 5 to 16 for real $x$.
$$
\frac{(2 x-1)}{3} \geq \frac{(3 x-2)}{4}-\frac{(2-x)}{5}
$$

Joshua Hale
Joshua Hale
Numerade Educator
01:08

Problem 17

Solve the inequalities in Exercises 17 to 20 and show the graph of the solution in each case on number line.
$$
3 x-2<2 x+1
$$

Brandon Fox
Brandon Fox
Numerade Educator
01:08

Problem 18

Solve the inequalities in Exercises 17 to 20 and show the graph of the solution in each case on number line.
$$
5 x-3 \geq 3 x-5
$$

Brandon Fox
Brandon Fox
Numerade Educator
01:08

Problem 19

Solve the inequalities in Exercises 17 to 20 and show the graph of the solution in each case on number line.
$$
3(1-x)<2(x+4)
$$

Brandon Fox
Brandon Fox
Numerade Educator
01:08

Problem 20

Solve the inequalities in Exercises 17 to 20 and show the graph of the solution in each case on number line.
$$
\frac{x}{2} \geq \frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}
$$

Brandon Fox
Brandon Fox
Numerade Educator
01:32

Problem 21

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.

Aman Gupta
Aman Gupta
Numerade Educator
02:04

Problem 22

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.

AG
Ankit Gupta
Numerade Educator
00:54

Problem 23

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

Victor Salazar
Victor Salazar
Numerade Educator
01:22

Problem 24

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23 .

Victor Salazar
Victor Salazar
Numerade Educator
02:49

Problem 25

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

Andrija Isakov
Andrija Isakov
Numerade Educator
01:25

Problem 26

A man wants to cut three lengths from a single piece of board of length $91 \mathrm{~cm}$. The second length is to be $3 \mathrm{~cm}$ 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 $5 \mathrm{~cm}$ 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, $x+(x+3)+2 x \leq 91$ and $2 x \geq(x+3)+5]$

Karly Williams
Karly Williams
Numerade Educator