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<x≤5 Solution set ={−3,−1,0,1,3}
(v)
−8<x<1 Solution set ={−7,−5,−3,−1,0}
(vi)
0≤x≤4 Solution set ={0,1,3}
Question 2
Sol :
It shown by thick dots on number line (i) x≤4,x∈N
(ii) x<5,x∈W
(iii) −3≤x<3,x∈L
Sol :
Replacement Set ={-6,-4,-2,0,2,4,6}
−4≤x<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+8≤23x≤2−83x≤−6x≤−2
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,x∈N14x<17−14x<16x<4,x∈N
As x∈N, the Solution set is {1,2,3}
(ii) 4x+1≤17,x∈W4x≤17−14x≤16x≤4
As x∈W, the solution set is {0,1,2,3,4}
(iii) 4>3x−11,x∈N3x−11<43x<4+1133x<15x<5
As x∈N, the solution set is {1,2,3,4}
(iv)−17≤9x−8,x∈z
9x−8≥−17
9x≥−17+8
9x≥−9
x≥−1
As x+z, the solution set is {-1,0,1,2,3 ...}
Question 7
Sol :
(i) 2y−15≤2,y∈N
2y−1≤10
2y≤10+1
2y≤11
y≤112
As y∈N, the solution set is {1,2,3,4,5}
(ii) 2y+13+1≤3,y∈w
2y+13≤3−1
2y+13≤2
2y+1≤6
2y+6−1
2y≤5
y≤52
As y∈W, the solution set is {0,1,2}
(iii) 23p+s<9,p∈W.
23p<9−5
213<4
2 p<12
p<6
As p∈W, the solution set is {0,1,2,3,4,5}
(iv) −2(p+3)>5p∈I
Multiplying '- ' on both sides
2(p+3)<-5
2 p+6<-5
2 p<-5-6
2 p<-11
p<−112
As p∈I, the solution set is {...-9,-8,-7,-6}
Question 8
Sol :
(i) 2x−3<x+2,x∈N
2x<x+2+3
2 x-x<5
x<5
As x∈N, the Solution set is {1,2,3,4}
(ii) 3−x≤5−3x,x∈W
3−x+3x≤5
2x+3≤5
2x≤5−3
2x≤2
x≤1
As x∈W, the solution set is {0,1}
(iv) 32−x2>−1,x∈N
3−x2>−1
3-x>-2
Multiplying with '- ' on son sides
x-3<2
x<2+3
x<5
As x∈N, the solution set is {1,2,34}
Question 9
Sol :
{-3,-2,-1,0,1,2,3}
{-3,-2,-1,0,1,2,3}
3x−12<23x−1<43x−4<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,x∈w
x3−x6+14<12
x3−x6<12−14
2x−x6<2−14
x6<14
x<64
x<32
As x∈W, the solution set is {0,1}
Question 11
Sol :
(i)
−4≤4x<14,x∈N4x⩾−4;4x<14x⩾−1;x<14/4x<7/2
As x∈N, the solution set is {-1,0,1,2,3}
(ii) −1<x2+1≤3,x∈I
x2+1>−1;12+1≤3
x2>−1−1;x2≤3−1
x2>−2;x2≤2
x>−4;x≤4
i.e −4<x≤4
As x∈I, the solution set is {-3,-2,-1,0,1,2,3,4}
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