S.chand publication New Learning Composite mathematics solution of class 8 Chapter 7 Linear Equations Exercise 7A

 Exercise 7A

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Q1 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 1

8x+14=5x+44

Sol :

⇒8x-5x=44-14

⇒3x=30

⇒x=10

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Q2 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 2

5m+7=10m–3

Sol :

⇒10m-5m=7+3

⇒5m=10

⇒m=2

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Q3 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 3

8y–14=6–2y

Sol :

⇒8y+2y=6+14

⇒10y=20

⇒y=2

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Q4 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 4

6p–21=p+4

Sol :

⇒6p-p=4+21

⇒5p=25

⇒p=5

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Q5 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 5

2(x–1)=12

Sol :

⇒2x-2=12

⇒2x=12+2

⇒x=7

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Q6 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 6

7+3(t+5)=31

Sol :

⇒7+3t+15=31

⇒3t=31-15-7

⇒3t=31-22=9

⇒t=3

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Q7 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 7

15+3(4x–30)=33

Sol :

⇒15+2x-90=33

⇒12x=33+90-15

⇒12x=90+18=108

⇒x=9

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Q8 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 8

5(x+2)–9(x–2)=0

Sol :

⇒5x+10-9x+18=0

⇒-4x=-(18+10)

⇒4x=28

⇒x=7

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Q9 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 9

3x+5=0.5x – 7

Sol :

⇒3x-0.5x=-7-5

⇒$\frac{25x}{10}=-12$

⇒$x=\frac{-12\times 10}{25}=\frac{-24}{5}$

⇒x=-4.8

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Q10 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 10

0.1(t–3)=0.15(t–4)

Sol :

⇒0.1t-0.3=0.15t-0.60

⇒+0.60-0.3=0.15t-0.1t

⇒0.30=0.05t

⇒t=6

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Q11 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 11

2(x – 2) + 5 = 4(x – 6) + 3

Sol :

⇒2x-4+5=4x-24+3

⇒-4+5+24-3=4x-2x

⇒-4-3+29=2x

⇒-7+29=2x

⇒22=2x

⇒x=11

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Q12 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 12

2m(m – 4) – 8 = m(2m – 12)

Sol :

⇒2m²-8m-8=2m²-12m

⇒12m-8m=8

⇒4m=8

⇒m=2

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Q13 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 13

3a + 2(a – 9) = 6 – (2a – 3)

Sol :

⇒3a+2a-18=6-2a+3

⇒5a+2a=18+9

⇒7a=27

⇒$a=\frac{27}{7}$

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Q14 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 14

8x – 2(2 + 3x) = 2(1 – 2x) – 3(x – 1)

Sol :

⇒8a-4-6x=2-4x-3x+3

⇒2x+7x=5+4=9

⇒9x=9

⇒x=1

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Q15 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 15

$\frac{x}{2}+\frac{x}{3}+\frac{x}{6}=18$

Sol :

⇒$\frac{3x+2x+x}{6}=18$

⇒6x=18×6

⇒$x=\frac{18\times 6}{6}=18$

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Q16 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 16

$\frac{2x}{3}+\frac{x}{4}+\frac{x}{2}=34$

Sol :
⇒$\frac{16x+6x+12x}{24}=34$

⇒34x=34×24

⇒x=24

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Q17 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 17

$\frac{p+1}{2}-\frac{2(p-1)}{3}=0$

Sol :

⇒$\frac{3(p+1)-4(p-1)}{6}=0$

⇒3p+3-4p+4=0

⇒-p+7=0

⇒p=7

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Q18 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 18

$6-\frac{3(n-7)}{4}=\frac{n}{2}$

Sol :

⇒$\frac{-3n+21}{4}=\frac{n}{2}-6$
⇒$\frac{-3n}{4}+\frac{21}{4}=\frac{n}{2}-6$
⇒$\frac{3n}{4}+\frac{n}{2}=\frac{21}{4}+6$
⇒$\frac{3n+2n}{4}=\frac{21+24}{4}$
⇒5n=45

⇒$n=\frac{45}{5}$

⇒n=9

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Q19 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 19

$10-\frac{5(1+x)}{3}+\frac{3x+1}{5}=0$

Sol :

⇒$10-\frac{(5+5x)}{3}+\frac{3x+1}{5}=0$

⇒$\frac{-5}{3}-\frac{5x}{3}+\frac{3x}{5}+\frac{1}{5}=-10$

⇒$\frac{-5x}{3}+\frac{3x}{5}=-10-\frac{1}{5}+\frac{5}{3}$

⇒$\frac{-25x+9x}{15}=\frac{-128}{15}$
⇒-16x=-128
⇒x=8

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Q20 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 20

$\frac{2b+1}{5}-\frac{b-1}{3}=1$

Sol :

⇒$\frac{6b+3-5b+5}{15}=1$

⇒b+8=15

⇒b=15-8=7

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Q21 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 21

$\frac{5(1-z)}{3}-\frac{(3z-1)}{5}=\frac{1}{6}$

Sol :
⇒$\frac{5}{3}-\frac{5z}{3}-\frac{3z}{5}+\frac{1}{5}=\frac{1}{6}$

⇒$\frac{-25z-9z}{15}=\frac{1}{6}-\frac{5}{3}-\frac{1}{5}$

⇒$\frac{-34z}{15}=\frac{(1\times 5)-(5\times 10)-1\times 6}{30}$

⇒$\frac{-34z}{15}=\frac{5-50-6}{30}$

⇒$\frac{-34z}{15}=\frac{5-56}{30}$

⇒$-34z=\frac{-51}{30}\times 15$

⇒$z=\frac{-51}{2 \times -34}$

⇒$z=\frac{51}{68}=\frac{3}{4}$

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Q22 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 22

$\frac{x+5}{15}-\frac{x-5}{10}=1+\frac{2x}{15}$

Sol :

⇒$\frac{x}{15}+\frac{5}{15}-\frac{x}{10}+\frac{5}{10}=1+\frac{2x}{15}$

⇒$\frac{x}{15}-\frac{x}{10}-\frac{2x}{15}=-\frac{1}{3}-\frac{1}{2}+\frac{1}{1}$

⇒$\frac{2x-3x-4x}{30}=\frac{-2-3+6}{6}$

⇒$\frac{2x-7x}{30}=-\frac{1}{6}$

⇒$\frac{-5x}{30}=-\frac{1}{6}$

⇒$-\frac{x}{6}=\frac{1}{6}$

⇒-x=1

⇒-(-x)=-1

⇒x=1

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Q23 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 23

$\frac{3x-4}{6}-\frac{2x+3}{8}=\frac{2x-7}{24}$

Sol :
⇒$\frac{12x-16-6x-9}{24}=\frac{2x-7}{24}$

⇒12x-16-6x-9=2x-7

⇒12x-6x-2x=-7+25

⇒12x-8x=+18

⇒4x=18

⇒$x=\frac{18}{4}=\frac{9}{2}$

 

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Q24 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 24

$(x+0.5) +\frac{1}{2}\left(3x – \frac{1}{3}\right) = \frac{1}{3}(x+1)$

Sol :
⇒$x+0.5+\frac{3x}{2}-\frac{1}{6}=\frac{x}{3}+\frac{1}{3}$

⇒$x+\frac{3x}{2}-\frac{x}{2}=\frac{1}{3}+\frac{1}{6}-0.5$

⇒$\frac{2x+3x-x}{2}=\frac{1}{3}+\frac{1}{6}-\frac{1}{2}$

⇒$\frac{4x}{2}=\frac{3-3}{6}$

⇒$\frac{4x}{2}=0$

⇒x=0

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Q25 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 25

$\frac{9x-5}{7}=\frac{6x+2}{5}$

Sol :

⇒45x-25=42x+14

⇒45x-42x=14+25

⇒3x=39

⇒x=13

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Q26 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 26

$\frac{7x-10}{5}=\frac{8x-5}{7}$

Sol :

⇒49x-70=40x-25

⇒49x-40x=70-25=45

⇒9x=45

⇒x=5

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Q27 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 27

$\frac{2x-7}{x+4}=\frac{3}{4}$

Sol :

⇒4(2x-7)=3(x+4)

⇒8x-28=3x+12

⇒8x-3x=28+12

⇒5x=40

⇒$x=\frac{40}{5}=8$

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Q28 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 28

$\frac{3m+4}{2-6m}=\frac{-2}{5}$

Sol :

⇒15m+20=-4+12m

⇒15m-12m=-4-20

⇒3m=-24

⇒m=-8

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Q29 | Ex-7A | Class 8 | Linear Equations | S.chand |New Learning Composite Mathematics| myhelper

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Question 29

$\frac{2n-3}{2n-1}=\frac{3n-1}{3n+1}$

Sol :

⇒(2n-3)(3n+1)=(2n-1)(3n-1)

⇒6x²+2n-9n-3=6x²-2n-3n+1

⇒-7n+5n=1+3

⇒-2n=4
⇒n=-2