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S.chand books class 8 maths solution chapter 15 Linear Equations exercise 15 A

EXERCISE 15 A


Solve the following equations:

Question 1

3(x+1) + 4x = 24
Sol :

⇒ 3x+3+4x=24

⇒ 7x=24-3

⇒ 7x=21

x=\dfrac{21}{7}

x=3

 


Question 2

16-2(3y+5) = 4(y-2)
Sol:

⇒16-6y-10=4y-8

⇒16-10+8=4y+6y

⇒24-10=10y

⇒14=10y

y=\dfrac{14}{10}

⇒y=1.4

 


Question 3

3(z+1)+4(z+0.3) = 20z + 0.98
Sol:

⇒3z+3+4z+1.2=20z+0.98

⇒7z+4=20z+0.98

⇒4-0.98=20z-7z

⇒3.02=13z

z=\dfrac{3.02}{13}

⇒z=0.23

 


Question 4

7m-4(m+6) = 7(m-8)+4

Sol :

⇒7m-4m-24=7m-56+4

⇒3m-24=7m-52

⇒52-24=7m-3m

⇒28=4m

m=\dfrac{28}{4}

⇒m=7

 


Question 5

\dfrac{x}{2}+\dfrac{x}{3} = 15

Sol :

Take L.C.M of 2 and 3 = 6

\dfrac{x\times 3 + x\times 2}{6}=15

\dfrac{3x+2x}{6}=15

\dfrac{5x}{6}=15

x=\dfrac{15\times 6}{5}

⇒x=18

 


Question 6

\dfrac{4(x+2)}{5}=7+\dfrac{5x}{13}

Sol :
\dfrac{4x+8)}{5}=7+\dfrac{5x}{13}

\dfrac{4x+8}{5}=\dfrac{7\times 13+5x}{13}

\dfrac{4x+8}{5}=\dfrac{91+5x}{13}

⇒13(4x+8)=5(91+5x)

⇒52x+104=455+25x

⇒52x-25x=455-104

⇒27x=351

x=\dfrac{351}{27}

⇒x=13

 


Question 7

\dfrac{x+3}{2}-\dfrac{4}{3}=\dfrac{3x-7}{3}

Sol :
L.C.M of 2 and 3 is 6

\dfrac{3(x+3)-2(4)}{6}=\dfrac{3x-7}{3}

\dfrac{3x+9-8}{6}=\dfrac{3x-7}{3}

\dfrac{3x+1}{6}=\dfrac{3x-7}{3}

⇒3(3x+1)=6(3x-7)

⇒9x+3=18x-42

⇒42+3=18x-9x

⇒9x=45

x=\dfrac{45}{9}

⇒x=5

 


Question 8

\dfrac{5x+1}{2}-\dfrac{x-2}{6}=\dfrac{2x+4}{3}
Sol :
L.C.M of 2 and 6 is 6

\dfrac{3(5x+1)-(x-2)}{6}=\dfrac{2x+4}{3}

\dfrac{15x+3-x+2}{6}=\dfrac{2x+4}{3}

\dfrac{14x+5}{6}=\dfrac{2x+4}{3}

⇒3(14x+5)=6(2x+4)

⇒42x+15=12x+24

⇒42x-12x=24-15

⇒30x=9

x=\dfrac{9}{30}

x=\dfrac{3}{10}

 


Question 9

\dfrac{9x-5}{7}=\dfrac{6x+2}{5}
Sol :

⇒5(9x-5)=7(6x+2)

⇒45x-25=42x+14

⇒45x-42x=14+25

⇒3x=39

x=\dfrac{39}{3}

⇒x=13

 


Question 10

\dfrac{9x}{7-6x}=2
Sol :

⇒2(7-6x)=9x

⇒14-12x=9x

⇒14=9x+12x

⇒14=21x

x=\dfrac{14}{21}

x=\dfrac{2}{3}

 


Question 11

\dfrac{2x-1}{3x+1}=\dfrac{6x-1}{9x-3}
Sol:

⇒(2x-1)(9x-3)=(6x-1)(3x+1)

⇒2x.9x-9x+3=6x.3x-3x-1

⇒18x2-9x+3=18x2-3x-1

⇒18x2-18x2-9x+3x+3-1=0

⇒-6x+2=0

⇒2=6x

x=\dfrac{2}{6}

 


Question 12

\dfrac{(1-3y)(4-y)}{(2-3y)(1-y)}=1
Sol :

\dfrac{4-y - 3y.4 - 3y.-y}{2-2y - 3y + 3y.y}=1

\dfrac{4-y-12y+3y^2}{2-2y-3y+3y^2}=1

\dfrac{4-11y+3y^2}{2+5y+3y^2}=1

⇒4-11y+3y2=1(2+5y+3y2)

⇒4-11y+3y2=2+5y+3y2

⇒4-2-11y-5y+3y2-3y^2=0

⇒2-6y=0

⇒2=6y

y=\dfrac{2}{6}

y=\dfrac{1}{3}

 


Question 13

\dfrac{(4x+4)-(7x-8)}{4x+5}=-\dfrac{4}{3}
Sol :

\dfrac{4x+4-7x+8}{4x+5}=-\dfrac{4}{3}

\dfrac{-3x+12}{4x+5}=-\dfrac{4}{3}

⇒3(-3x+12)=-4(4x+5)

⇒-9x+36=-16x-20

⇒16x-9x=-20-36

⇒7x=-56

⇒x=-8

 


 

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