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