KC Sinha Mathematics Solution Class 11 Chapter 13 Linear Inequalities Exercise 13.2

 Exercise 13.2

Page no 13.31

Type 1

Question 1

Solve the following inequations :

1. $-2 \leq 6 x-1<2$

2. $-3 \leq 4-7 x<18$

3. $0<-\frac{x}{3}<1$

4. $-7<2 x-3<7$

5. $6 \leq-3(2 x-4)<12$

6. $-2<1-3 x<7$

7. $-3 \leq \frac{4-7 x}{2} \leq 18$

8. $-12 \leq \frac{4-3 x}{-5}<2$

Question 9

Find the range of values of $x$, which satisfy the inequality $-\frac{1}{5} \leq \frac{3 x}{10}+1<\frac{2}{5}, x<R$. Represent the solution set on the number line.

Question 10

Find the values of $x$, which satisfy the inequation :

$-2 \leq \frac{1}{2}-\frac{2 x}{3} \leq 1 \frac{5}{6}, x \in N$

Represent the solution set on the number line.

Type 2

Question 11

Solve the following system of inequations :

11. $2 x+5 \leq 0, x-3 \leq 0$

12. $x-2>0,3 x<18$

13. $x+3>0,2 x<14$

14. $x+2>11,2 x \leq 20$

15. $5 x+1>-24,5 x-1<24$

16. $3 x-1 \geq 5, x+2>-1$

17. $2 x-7<11,3 x+4<-5$

18. $4 x-5<11,-3 x-4 \geq 8$

19. $4-5 x>-11,4 x+11 \leq-13$

20. $-4 x+1 \geq 0,3-4 x<0$

21. $x+2 \leq 5,3 x-4>-2+x$

22. $4 x+3 \geq 2 x+17,3 x-5<-2$

23. $7 x-8<4 x+7,-\frac{x}{2}>4$

24. $3 x-7>2(x-6), 6-x>11-2 x$

25. $2 x-7>5-x, 11-5 x \leq 1$

26. $\frac{4 x}{3}-\frac{9}{4}<x+\frac{3}{4}, \frac{7 x-1}{3}-\frac{7 x+2}{6}>x$

Page no 13.32

Type 3

Question 27

Solve the following inequations :

27. (i) $|x| \leq 5$

(ii) $|x|>5$

28. (i) $|x-2| \leq 5$

(ii) $|x+1| \geq 3$

29. $|3 x-2| \leq \frac{1}{2}$

30. $1 \leq|x+1| \leq 2$

31. $\frac{|x+3|+x}{x+2}>1$

32. $|x-1|+|x-2| \geq 3$

33. $|x+1|+|x-1|=|2 x|$

34. $|x+2|-|x|=2$