ML AGGARWAL CLASS 8 Chapter 12 Linear Equations and Inqualities In one Variable Exercise 12.3

 Exercise 12.3

Question 1

Sol :
(i) x>-2
Solution set ={-1,0,1,3}

(ii) x<-2
Solution set ={-7,-5,-3}

(iii) x>2
Solution set ={3}

(iv)
5<x5 Solution set ={3,1,0,1,3}

(v) 
8<x<1 Solution set ={7,5,3,1,0}

(vi) 
0x4 Solution set ={0,1,3}

Question 2

Sol :
It shown by thick dots on number line 

(i) x4,xN




(ii) x<5,xW




(iii) 3x<3,xL




Question 3

Sol :
Replacement Set ={-6,-4,-2,0,2,4,6}

4x<4




Question 4

Sol :
(i) {1,2,3 ...10}





(ii) {-1,0,1,2,5,8}




(iii) {-5,10}





(iv) {5,6,7,8,9,10}




Solution Set=ϕ

Question 5

Sol :
(i) 2 x-3>7
2 x>7+3
2 x>10
x>5

Solution set ={6,9,12}


(ii) 3x+823x283x6x2

Solution set ={-6,-3}


(iii) -3<1-2 x
3>2 x-1
2 x-1<3
2 x<3+1
2 x<4
x<2

Solution set ={-6,-3,0}

Question 6

Sol :
(i) 4x+1<17,xN14x<1714x<16x<4,xN

As xN, the Solution set is {1,2,3}


(ii) 4x+117,xW4x1714x16x4

As xW, the solution set is {0,1,2,3,4}


(iii) 4>3x11,xN3x11<43x<4+1133x<15x<5

As xN, the solution set is {1,2,3,4}


(iv)179x8,xz

9x817

9x17+8

9x9

x1

As x+z, the solution set is {-1,0,1,2,3 ...}

Question 7

Sol :
(i) 2y152,yN

2y110

2y10+1

2y11

y112

As yN, the solution set is {1,2,3,4,5}


(ii) 2y+13+13,yw

2y+1331

2y+132

2y+16

2y+61

2y5

y52

As yW, the solution set is {0,1,2}


(iii) 23p+s<9,pW.

23p<95

213<4

2 p<12
p<6

As pW, the solution set is {0,1,2,3,4,5}


(iv) 2(p+3)>5pI
Multiplying '- ' on both sides

2(p+3)<-5
2 p+6<-5
2 p<-5-6
2 p<-11

p<112

As pI, the solution set is {...-9,-8,-7,-6}

Question 8

Sol :
(i) 2x3<x+2,xN
2x<x+2+3
2 x-x<5
x<5

As xN, the Solution set is {1,2,3,4}


(ii) 3x53x,xW

3x+3x5

2x+35

2x53

2x2

x1

As xW, the solution set is {0,1}


(iv) 32x2>1,xN

3x2>1

3-x>-2

Multiplying with '- ' on son sides

x-3<2
x<2+3
x<5

As xN, the solution set is {1,2,34}

Question 9

Sol :
{-3,-2,-1,0,1,2,3}
3x12<23x1<43x4<4+13x<5

x<5/3

As x should be in replacement set, the solution

set is {-3,-2,-1,0,1}




Question 10

Sol :
x3+14<x6+12,xw

x3x6+14<12

x3x6<1214

2xx6<214

x6<14

x<64

x<32

As xW, the solution set is {0,1}

Question 11

Sol :
(i) 
44x<14,xN4x4;4x<14x1;x<14/4x<7/2

As xN, the solution set is {-1,0,1,2,3}





(ii) 1<x2+13,xI

x2+1>1;12+13

x2>11;x231

x2>2;x22

x>4;x4

i.e 4<x4

As xI, the solution set is {-3,-2,-1,0,1,2,3,4}




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