5. 25 - 4x i 16. Find the smallest value of x when (I) I € R, (i.!.) I € Z.

6. 19 -4x i 3, x € prime numbers less than 15

Ill. Solve the following inequations. Represent the solution set on the number line.
1.1S25-2x<5x-40, x€Z 2. -8Sx-7S2(2-x), x€W

3.llS;15-2y<23, yez 4. 12 2 2 - 53/ > 2ty - 2) -y, y€I

5. -2 < i - qu s35, xeR 6.-2s;2x-3<1, x€R

24

7.-5<2x+1S5, XER 8.-2<3-2xS;5, XER

9.-5<x-2S;7-2x, xeN ]o. _]Z < r+i < 45, x € w

33

11. -2< i-± S 1: , x e N 12. =S%+1<±, x€R

32 55

IV. Solve for # and write the solution set for the following inequations and represent it on the
number line.
1.1215-7x>2x-27, x€R 2.2-x<5-2x<x-1, x€R

3. 3x+±>4£-222x-4, x€R 4.I-2<3(x-2)+5<8-I, x€R

33

5.4x-3S2r+7<6r-1, fez 6. 22-2x21+x>4-x, xel

7. x-3S¥+2<2%+¥,x€I [2009] 8. 13x-5< 15x+4 < 7x + 12, xe R [2015]

Solve for # and write the solution set for the following inequations (Qs 1-5). Also represent it on the
number line.
1.-15<1-4r<9, x€Z 2. i-4<4£-2<¥-1, x€R
33
3. -2< i-2£ < 1:, x € N [2001] 4. -:=Z-15=:, r€R
23
5.x+5S=2x+3<12-x, xeN

6. Find P fl Q and represent on the number line.

P={r:8x-1>5x+2, %€N}andQ={r:7x-223(x+6), r€N}
7. A = {x : -3 sS x S 5, x E R}, 8 = {x .. -1 < x < 8, r € R}. Represent

(z.) A r` B (z.z.) A r` B' on different number lines.

Write down:
(z.z.z.) the least value of A rl 8' (z.zJ) the greatest value of A r\ 8.

Linear Inequations
@
8. Solve the following inequation and represent the solution set on the number line.

4x-19<±-2Sx-3, reR [2012]

5

9. Given A = {x : -1 < 2x -5 < 11, I € R}, 8 = {x : -11 < 3x -2 S: 10, x E R}

(I.) Represent A and 8 on number lines.

(!.!.) Also represent A rl 8 on the number line.
10. Find the values of I, which satisfy the inequation.

-3E<l-4£<2:,x€I.Graphthesolutionsetonthenumberline.
663

1. Solve the following inequation, and graph the -2Z s "1 < 3:;xeR [2007]
solution set, on the number line: 33
2x-3<x+2<3x+5,x €R. [1998]
10. Solve the given inequation and graph the solution
on the number line:
2. Solve the inequation:
2y-3<y+1<fty+7;y€ R. [2008]
12 + 1 i r S 5 + 3x, x e R. 11. Solve the following inequation and represent the
6
solution set on the number line:
Represent the solution on a number line. [1999]
3. Solve the inequation: -3 < 3 - 2x < 9, x € R.
-3 < -i-¥ = :, I e R. [2010]
Represent your solution on a number line. [2000]
12. Solve the following inequation and represent the
4. Solve the following inequatiori, and graph the
solution set on the number line:
solution on the number line:
2x-5<5x+4<11,wherex e I [2011]
2x-5<5x+4<11,I €R [2002]
13. Solve the following inequation, write the solution
5. Solve 2 < 2x - 3 < 5, x € R and mark it on a number
set and represent it on the number line:
line. [2003]
6. Given that x € I, solve the inequation and graph -€SZ-]5<:; XeR [2ol3]
the solution on the number line:
14. Find the values of x, which satisfy the inequation
3 2 ±=±+± 2 2 [2004]
23
-2 i < 1 - 2£ < 2, x e W. Graph the solution
623
7. A = {x : llx -5 > 7x + 3, x € R} and
8 = {x : 18x -9 2 15 + 12x, I e R}. set on the number line. [2014]
Find the range of Set A r` 8 and represent it on a 15. Solve the following inequation and write the
number line. [2005] solution set:
8. Given that x e R, solve the following inequality x+1
-3(x-7)215-7x>T,X€R
and graph the solution on the number line:
-1 i 3+4x<23 [2006] Represent the solution on a real number line.

9. Solve the following inequation and graph the [2016]

solution on the number line.

ICSE Mathematics-X