MATHEMATICS IN EVERYDAY LIFE–8

MATHEMATICS IN EVERYDAY LIFE?8

Chapter 8 : Linear Equations in One Variable

ANSWER KEYS

EXERCISE 8.1

1. x ? 3 = 8

x =8 + 3

(By transposing ? 3)

x = 11

2. x + 7 = 15

x = 15 ? 7

(By transposing 7)

x=8

3. 5x = 20 Dividing both sides by 5, we get

5x 5

=

20 5

x=4

4. 2x + 6 = 10

2x = 10 ? 6

2x = 4

(By transposing 6)

2x 4

2 =2

(On dividing both sides by 2)

x=2

5. 7x ? 5 = 16

7x = 16 + 5

7x = 21

(By transposing ? 5)

7x 21 7 = 7 (On dividing both sides by 7)

x=3

3x 6. 2 = 18

Multiplying both sides by 2, we get

3x 2 ? 2 = 18 ? 2

3x = 36

3x 36

3 = 3 (On dividing both sides by 3)

x = 12

Mathematics In Everyday Life-8

x 7. 5 = 7

x ?5=7?5 5 (On multiplying both sides by 5)

x = 35

8.

4 7

+ x =

20 7

x =

20 7

?

4 7

(By transposing

4 7)

20 4

x= 7

x = 16

7

9. 7 = 2x ? 5

or 2x ? 5 = 7

2x = 7 + 5

2x = 12

(By transposing ? 5)

2x = 12 (On dividing both sides by 2)

22

x=6

10. 1.6x + 2 = 5.2

1.6x = 5.2 ? 2

1.6x = 3.2

(By transposing 2)

1.6x 3.2 1.6 = 1.6 (On dividing both sides by 1.6)

x=2

11. 13 + 2a = 39

2a = 39 ? 13

2a = 26

(By transposing 13)

2a = 26

(On dividing both sides by 2)

22

a = 13

1

12. 16a ? 4 = 28

16a = 28 + 4

16a = 32

(By transposing ? 4)

16a 32 16 = 16 (On dividing both sides by 16)

a=2

EXERCISE 8.2

1. 2x ? 5 = 3x + 5

Transposing variables on L.H.S. and constant terms on R.H.S., we get

2x ? 3x = 5 + 5

? x = 10

x = 10 (On multiplying both sides by ? 1)

2. 9x + 15 = 20 ? x

Transposing variables on L.H.S. and constant terms on R.H.S., we get

9x + x = 20 ? 15

10x = 5

10x 10

=

5 10

(On dividing both sides by 10)

x= 1

2

3

4

3. 2m ? 5 = m + 5

Transposing variables on L.H.S. and constant terms on R.H.S., we get

2m ? m =

4 5

+

3 5

m=7

5

4. 3m + 4 = 8m + 24

Transposing variables on L.H.S. and constant terms on R.H.S., we get

3m ? 8m = 24 ? 4

? 5m = 20

5m 20 5 =5

(On dividing both sides by 5)

? m =4

m = 4 (On multiplying both sides by ? 1)

m 5. 2 + 6 = m ? 8

Transposing variables on L.H.S. and constant terms on R.H.S., we get

2

m 2 ?m= ?8?6

m = ? 14

2

(?

2)

m 2

=

(? 14) ? (?

2)

(On multiplying both sides by ? 2)

m = 28

6. 7 ? x = 4 ? x 3

Transposing variables on L.H.S. and constant terms on R.H.S., we get

? x +x=4?7 3

x 3x = ? 3 3

2x 3

=? 3

2x 3 ? 3 = ? 3 ? 3 (On multiplying both sides by 3)

2x = ? 9

2x = 9 (On dividing both sides by 2)

22

x= 9

2

72 7. 3t + 5 = 5 + 5t

or 2 + 5t = 3t + 7

5

5

Transposing variables on L.H.S. and constant terms on R.H.S., we get

72 5t ? 3t = 5 ? 5

2t

=

5 5

2t = 1

2t 2

=

1 2

(On dividing both sides by 2)

t= 1

2

8. 3.5x ? 9 = 2.4x + 13

Transposing variables on L.H.S. and constant terms on R.H.S., we get

Answer Keys

3.5x ? 2.4x = 13 + 9

1.1x = 22

1.1x 22

1.1 = 1.1 (On dividing both sides by 1.1)

x = 20

4

5

9. 11x ? 3 = 2x + 3

Transposing variables on L.H.S. and constant terms on R.H.S., we get

54 11x ? 2x = 3 + 3

9

9x = 3

9x = 3

9x 9

=

3 9

(On dividing both sides by 9)

x= 1

3

10.

12x ? 2 7

13 = 14 ? 5x

Transposing variables on L.H.S. and constant terms on R.H.S., we get

13 2 12x + 5x = 14 + 7

17x = 17

14

17x 17

=

17 14 17

(On dividing both sides by 17)

x= 1

14

EXERCISE 8.3

4x 1 1. 5x 2 = 1

4x ? 1 = 5x + 2

? 1 ? 2 = 5x ? 4x

?3=x

x=3

(By cross multiplication) (By transposing)

Verification: L.H.S. = 4( 3) 1 = 12 1 5( 3) 2 15 2

= 13 = 1 = R.H.S. 13

Mathematics In Everyday Life-8

2.

x 5 3 2x

=

5 3

3(3x + 5) = 5(3 ? 2x)

9x + 15 = 15 ? 10x

9x + 10x = 15 ? 15

19x = 0

0 x = 19 = 0

x=0

(By cross multiplication) (By transposing)

Verification: L.H.S. =

3(0) 5 3 2(0)

=

05 30

= 5 = R.H.S. 3

2x 3 9 3. 3x 2 = 7

7(2x + 3) = 9(3x + 2)

14x + 21 = 27x + 18

21 ? 18 = 27x ? 14x

13x = 3

3 = 13x

(By cross multiplication) (By transposing)

13x 13

=

3 13

(On dividing both sides by 13)

x= 3

13

Verification: L.H.S. =

2

3 13

3

=

6 3 13

3

3 13

2

9 13

2

6 39 45

=

13 9 26

=

13 35

13

13

= 45 = 9 = R.H.S. 35 7

4. (3x 4) 2x = ? 9

(2 5x) 7x

58

3x 4 2x 2 5x 7x

=?

9 58

x4 =? 9

2 12x

58

58(x + 4) = ?9(2 ? 12x)

(By cross multiplication)

58x + 232 = ? 18 + 108x

3

 58x ? 108x = ? 18 ? 232

(By transposing)

? 50x = ? 250

50x = 250

50 50

(On dividing both sides by ?50)

x=5

Verification: L.H.S. = (3 5 4) 2 ? 5 (2 5 ? 5) 7 ? 5

= (15 4) 10 = 19 10 (2 25) 35 23 35

= 9 = ? 9 = R.H.S.

58

58

1

1

5. 2 (m ? 1) + 5 = 3 (2m + 1)

Multiplying both sides by 6, the L.C.M. of 2 and 3,

we get

6 ? 1 (m ? 1) + 6 ? 5 = 6 ? 1 (2m + 1)

2

3

3(m ? 1) + 30 = 2(2m + 1)

3m ? 3 + 30 = 4m + 2

? 3 + 30 ? 2 = 4m ? 3m

(By transposing)

25 = m

m = 25

Verification: L.H.S. = 1 (25 ? 1) + 5 = 1 ? 24 + 5

2

2

= 12 + 5 = 17

R.H.S. = 1 (2 ? 25 + 1) = 1 (50 + 1)

3

3

= 1 ? 51 = 17 3

L.H.S. = R.H.S.

6. 5x = ? 5 3x 4

5x = ? 5(3x + 4)

5x = ? 15x ? 20

5x + 15x = ? 20

20x = ? 20

(By cross multiplication) (By transposing)

20x = 20 (On dividing both sides by 20)

20 20

x=1

Verification: L.H.S. = 5 ? ( 1) = 5 3 ? ( 1) 4 3 4

= 5 = ? 5 = R.H.S. 1

4

2y 7. 3y 1 = ? 3

2y = ? 3(3y + 1)

2y = ? 9y ? 3

2y + 9y = ? 3

11y = ? 3

(By cross multiplication) (By transposing)

y = 3 (On dividing both sides by 11)

11

Verification: L.H.S. =

2

3 11

=

6 11

3

3 11

1

9 1 11

6

6

=

11 9 11

=

11 2

11

11

= 6 = ? 3 = R.H.S. 2

8.

1.2x 3 3.2x 6

=

9 8

8(1.2x + 3) = 9(3.2x + 6)

(By cross multiplication)

9.6x + 24 = 28.8x + 54

24 ? 54 = 28.8x ? 9.6x (By transposing)

? 30 = 19.2x

30

x = 19.2

(On dividing both sides by 19.2)

x = 300

192

x = 25

16

Verification: L.H.S. =

1.2

?

25 16

3

3.2

?

25 16

6

=

30 3 16 80 6 16

30 48 18

=

16 80 96

=

16 16

16

16

= 18 = 9 = R.H.S. 16 8

Answer Keys

9.

4y 8 5y 8

=

5 6

6(4y + 8) = 5(5y + 8)

24y + 48 = 25y + 40

48 ? 40 = 25y ? 24y

8 =y

(By cross multiplication) (By transposing)

y=8

Verification: L.H.S. = 4 ? 8 8 = 32 8 5 ? 8 8 40 8

xb xb 10. a b = a b

= 40 = 5 = R.H.S. 48 6

(x + b) (a + b) = (a ? b) (x ? b)

(By cross multiplication)

ax + bx + ab + b2 = ax ? ab ? bx + b2

ax + bx ? ax + bx = ? ab + b2 ? ab ? b2

(By transposing)

2bx = ? 2ab

2ab

x = 2b

(On dividing both sides by 2b)

x=a

Verification: L.H.S. = a b = (a b) = ? 1

ab

a b

R.H.S. = a b = (a b) = ? 1

ab

a b

11. 7x 4 = ? 4

x 2

3

3(7x + 4) = ? 4(x + 2)

21x + 12 = ? 4x ? 8

21x + 4x = ? 8 ? 12

25x = ? 20

(By cross multiplication) (By transposing)

x = ? 20 (On dividing both sides by 25)

25

x= 4

5

Verification: L.H.S. =

7

4 5

4

42

=

28 4 5 4 2

5

5

28 20 8

=

5 4 10

=

5 6

5

5

= 8 = 4 = R.H.S.

6

3

Mathematics In Everyday Life-8

12.

17(2 x) 5(x 12) 1 7x 7x 1

= 8

34 17x 5x 60 1 7x 7x 1

=8

34 17x 5x 60

1 7x 1 7x

=8

34 17x (5x 60) = 8 (1 7x)

34 17x 5x 60

(1 7x)

=8

22x 26 = 8

1 7x

? 22x ? 26 = 8(1 ? 7x)

(By cross multiplication)

? 22x ? 26 = 8 ? 56x

? 22x + 56x = 8 + 26

(By transposing)

34x = 34

x=1

(On dividing both sides by 34)

Verification: L.H.S. =

17(2 1) 5(1 12) 17?1 7?11

= 17 ? 1 5 13 = 17 65 17 71 6 6

4x 3 0.05 13. 10x 9 = 0.25

= 17 65 = 48 = 8 = R.H.S.

6

6

4x 3 5 1 10x 9 = 25 = 5

5(4x ? 3) = 1(10x ? 9) 20x ? 15 = 10x ? 9 20x ? 10x = ? 9 + 15

(By cross multiplication) (By transposing)

10x = 6

x= 6 =3

10 5

(On dividing both sides by 10)

x= 3

5

5

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