ICSE Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books               Class 8: NTSE Preparation
--------------------------------------------------------------

 

Q. 1 If   x \in \{-3,-2,-1,0,1,2,3 \} , find the solution set of each of the following:

i) x+2<1

\Rightarrow x \leq -1

Therefore \ Solution \ set = \{-3,-2\}

\\

ii) 2x-1 < 4

\Rightarrow 2x < 5

\Rightarrow  x < \frac{5}{2}

Therefore \ Solution \ set = \{-3,-2,-1,0,1,2 \}

\\

iii)  2/3 x<1

\Rightarrow x<3/2

Therefore \ Solution \ set = \{-3,-2,-1,0,1 \}

\\

iv) 1-x>0

\Rightarrow x<1

Therefore \ Solution \ set = \{-3,-2,-1,0 \}

\\

v) 3-5x<-1

\Rightarrow 5x>4

\Rightarrow x>4/5

Therefore \ Solution \ set =\{ 1,2,3 \}

\\

vi) 2-3x>1

\Rightarrow 3x<1

\Rightarrow x<1/3

Therefore \ Solution \ set = \{-3,-2,-1,0 \} 

\\

vii) -6 \geq 2x-4

\Rightarrow 2x \leq 2

\Rightarrow x \leq 1

Therefore \ Solution \ set = \{-3,-2,-1,0,1 \}

\\

viii) 3x-5 \geq -12

\Rightarrow 3x \geq -7

\Rightarrow x \geq (-7)/3

Therefore \ Solution \ set =\{-2,-1, 0, 1, 2, 3 \}

\\

xi) 14-2x<6

\Rightarrow 2x>8

\Rightarrow x>4

Therefore \ Solution \ set = \phi 

\\

Q.2 If x \in N ; find the solution set of each of the following in equation: N=\{1, 2, 3, ... \}

i) 3x-8<0 m1x

\Rightarrow 3x<8 

\Rightarrow x<\frac{8}{3} 

Solution \ Set = \{1,2  \} 

\\

ii) 7x+3 \leq 17 

\Rightarrow 7x \leq 14 

\Rightarrow x \leq 2 

Solution \ Set = \{1,2 \} 

\\

iii) 5-x>1 

\Rightarrow x<4 

Solution \ Set = \{1,2,3 \} 

\\

iv) 1-3x>-4 

\Rightarrow 3x<5 

\Rightarrow x<\frac{5}{3} 

Solution \ Set = \{1 \} 

\\

v) \frac{3}{2}-\frac{x}{2}>-1 

\Rightarrow \frac{x}{2}<\frac{5}{2}  

\Rightarrow  x<5 

Solution \ Set = \{1,2,3,4 \} 

\\

vi) \frac{-1}{4} \leq \frac{1}{2} - \frac{2}{3}

\Rightarrow \frac{-3}{4} \leq \frac{-x}{3}  

\Rightarrow \frac{x}{3}  \leq \frac{3}{4}  

\Rightarrow  x \leq \frac{9}{4}

Solution \ Set = \{1,2 \} 

\\

Q.3 If x \in Z , find the solution set of the following in equations:  Z = \{...-3, -2, -1, 0, 1, 2, 3, ...\}

i) 9x-7 \leq 25+3x 

\Rightarrow  6x \leq 32

 \Rightarrow  x \leq \frac{32}{6}

Solution \ Set = \{...-3, -2, -1, 0, 1, 2, 3, 4, 5...\}

31

\\

\\

ii) -17<9x-8

 \Rightarrow  9x>-9

 \Rightarrow  x>-1

Solution \ Set =\{0, 1, 2, 3...\}

32

\\

\\

iii) -4(x+5)>10

 \Rightarrow  -4x>30

 \Rightarrow  x<\frac{(-15)}{2}

Solution \ Set = \{...-10, -9, -8 \}

33

\\

\\

iv) 4-3x<13+x

\Rightarrow  4x>-9

 \Rightarrow x>\frac{(-9)}{4}

Solution \ Set = \{-2, -1, 0, 1, 2, 3, ...\}

34

\\

\\

v) 5-4x<10-x

 \Rightarrow  -5<3x

 \Rightarrow  x >\frac{(-5)}{3}

Solution \ Set = \{-1, 0, 1, 2, ...\}

35

\\

\\

vi)  10-2(1+4x)<20 m2x

  \Rightarrow  10-2-20<8x

  \Rightarrow  8x>-12

  \Rightarrow  x>-3/2

Solution \ Set = \{-1, 0, 1, 2, ...\}

36

\\

\\

Q.4 Find the Solution Set of each of the following in equations and represent the solution on a real line.

\ \ i)\ \ \    1-4x\geq{}-1, x \in N

  \Rightarrow{} 4x\leq{}2

  \Rightarrow{} x\leq{} \frac{1}{2}

  Solution \ Set = \varnothing{}

 \\

\ \ ii)\ \ \   -3\leq{}4x+1<9, x \in N

  \Rightarrow{} -4\leq{}4x<8

  \Rightarrow{} -1\leq{}x<2

  Solution \ Set=\{-1,0,1\}

42

 \\

\ \ iii)\ \ \   0<2x-5<5, x \in W \ \ \ \ \ W= \{0,1,2,3\ldots{}.\}

  \Rightarrow{} 5<2x<10

  \Rightarrow{} \frac{5}{2}<x<5

  Solution \ Set= \{3,4\}

43

 \\

\ \ iv)\ \ \ -3< \frac{x}{2} - 1<1, x \in Z

  \Rightarrow{} -2<\frac{x}{2}<2

  \Rightarrow{} -4<x<4

  Solution \ Set = \{-3,-2,-1,0,1,2,3\}

44

\\

\ \ v)\ \ \   -4<\frac{2x}{5}+1<-3, x\in Z

  \Rightarrow{} -5<\frac{2x}{5}<-4

  \Rightarrow{} 25<2x<-20

  \Rightarrow{} \frac{-25}{2}<x<-10

  Solution \ Set = \{-12,-11\}

45

\\

\ \ vi)\ \ \   3+\frac{x}{4}<\frac{2x}{3}+5, x\in R

  \Rightarrow{}\frac{x}{4}<\frac{2x}{3}+2

  \Rightarrow{}\frac{2x}{3}-\frac{x}{4}>-2

  \Rightarrow{} 5x>-24

  \Rightarrow{} x>\frac{(-24)}{5}

  Solution \ Set= \{x\in R :x>\frac{(-24)}{5}\}

46

\\

\ \ vii)\ \ \   \frac{(3x+1)}{4}\leq{}\frac{(5x-2)}{3}, x\in R

  \Rightarrow{} 9x+3\leq{}20x-8

  \Rightarrow{} 11x\geq{}11

  \Rightarrow{} x\geq{}1

  Solution \ Set = \{x \epsilon{} R: x\geq{}1\}

47

\\

m3x\ \ viii)\ \ \   \frac{1}{3} (4x-1)+3\leq{}4+\frac{2}{5}(6x+2)+\frac{4}{5}

  \Rightarrow{}\frac{4}{3} x-\frac{1}{3}+3\leq{}4+\frac{12}{5} x+\frac{4}{5}

  \Rightarrow{} \frac{(-32)}{15}\leq{}\frac{16}{15} x

  \Rightarrow{} x\geq{}-2

  Solution \ Set = \{x \in R: x\geq{}-2\}

48

\\

 

ICSE Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books               Class 8: NTSE Preparation
--------------------------------------------------------------

 

Advertisements