KC Sinha Mathematics Solution Class 11 Chapter 13 Linear Inequalities Exercise 13.1

 Exercise 13.1

Page no 13.15

Type 1

Question 1

If $x$ is non-negative integer, solve the inequation :

$2-3 x<5-4 x$

Also show the solution set on number line.

Question 2

Solve the inequation $2(x-2)<3 x-2, x \in\{-2,-1,0,1,2,3,4\}$ Also show the solution set on the number line.

Question 3

Solve the inequation $30 x<200$, when

(i) $x$ is an integer

(ii) $x$ is a natural number.

Question 4

Solve the inequations

(a) $3 x+5<x-7$ (b) $5 x-3<3 x+1$ when :

(i) $x$ is an integer

(ii) $x$ is a real number

Question 5

Solve the following inequations :

(i) $x+10>4 x-5$

(ii) $4 x+3<6 x+7$

(iii) $3 x-7>x+3$

(iv) $x+12<4 x-2$

Question 6

Solve the following inequations :

(i) $3 x-10>5 x+1$

(ii) $3(x-2) \leq 5 x+8$

(iii) $5 x-1>3 x+7$

(iv) $3 x+17 \leq 2(1-x)$

Question 7

Solve the following inequations :

(i) $2-3 x \geq 2(x+6)$

(ii) $2(2 x+3)-10<6(x-2)$

(iii) $-(x-3)+4>-2 x+5$

Page no 13.16

Question 8

Solve the following inequations:

(i) $\frac{3(x-2)}{5} \geq \frac{5(2-x)}{3}$

(ii) $\frac{11-2 x}{5} \geq \frac{9-3 x}{8}+\frac{3}{4}, x \in N$

(iii) $\frac{4+2 x}{3} \geq \frac{x}{2}-3$

(iv) $\frac{3}{5} x-\frac{2 x-1}{3}>1, x \in W$

(v) $\frac{5 x}{2}+\frac{3 x}{4} \geq \frac{39}{4}$

Question 9

Solve the following inequations :

(i) $\frac{3}{x-2}<0$

(ii) $-\frac{1}{x+2}>0$

  Type 2

Question 10

 Solve the following inequations :

(i) $\frac{x-3}{x+5}>0$

(ii) $\frac{x-3}{x-5}>0$

Question 11

Solve the following inequations :

(i) $\frac{x-1}{x-3}<1$

(ii) $\frac{x+1}{x-7} \geq 2$