Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Class 8 RD Sharma Solutions – Chapter 9 Linear Equation In One Variable – Exercise 9.3 | Set 1

  • Last Updated : 07 Apr, 2021

Solve the following equations and verify your answer:

Question 1. (2x-3)/(3x+2) = -2/3

Solution:

Given:

Hey! Looking for some great resources suitable for young ones? You've come to the right place. Check out our self-paced courses designed for students of grades I-XII

Start with topics like Python, HTML, ML, and learn to make some games and apps all with the help of our expertly designed content! So students worry no more, because GeeksforGeeks School is now here!

 



(2x-3) / (3x+2) = -2/3

After cross-multiplication we will get,

3(2x – 3) = -2(3x + 2)

6x – 9 = -6x – 4

Now rearrange the above equation

6x + 6x = 9 – 4

12x = 5

x = 5/12

Now verify the given equation by putting x = 5/12

(2x-3) / (3x+2) = -2/3

x = 5/12

(2(5/12) – 3) / (3(5/12) + 2) = -2/3

((5/6)-3) / ((5/4) + 2) = -2/3

((5-18)/6) / ((5+8)/4) = -2/3

(-13/6) / (13/4) = -2/3

(-13/6) × (4/13) = -2/3

-4/6 = -2/3

-2/3 = -2/3



Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 2. (2-y)/(y+7) = 3/5

Solution:

Given:

(2-y) / (y+7) = 3/5

After cross-multiplication we will get,

5(2-y) = 3(y+7)

10 – 5y = 3y + 21

Now rearrange the above equation,

10 – 21 = 3y + 5y

8y = – 11

y = -11/8

Now verify the given equation, by putting y = -11/8

(2-y) / (y+7) = 3/5

y = -11/8

(2 – (-11/8)) / ((-11/8) + 7) = 3/5

((16+11)/8) / ((-11+56)/8) = 3/5

(27/8) / (45/8) = 3/5

(27/8) × (8/45) = 3/5

27/45 = 3/5

3/5 = 3/5

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 3. (5x – 7)/(3x) = 2

Solution:

Given:

(5x – 7) / (3x) = 2

After cross-multiplication we will get,

5x – 7 = 2(3x)

5x – 7 = 6x

5x – 6x = 7



-x = 7

x = -7

Now verify the given equation but putting x = -7

(5x – 7) / (3x) = 2

x = -7

(5(-7) – 7) / (3(-7)) = 2

(-35 – 7) / -21 = 2

-42/-21 = 2

2 = 2

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 4. (3x+5)/(2x + 7) = 4

Solution:

Given:

(3x+5) / (2x + 7) = 4

After cross-multiplication we will get,

3x + 5 = 4(2x+7)

3x + 5 = 8x + 28

3x – 8x = 28 – 5

-5x = 23

x = -23/5

Now verify the given equation by putting x =-23/5

(3x+5) / (2x + 7) = 4

x = -23/5

(3(-23/5) + 5) / (2(-23/5) + 7) = 4

(-69/5 + 5) / (-46/5 + 7) = 4

(-69+25)/5 / (-46+35)/5 = 4

-44/5 / -11/5 = 4

-44/5 × 5/-11 = 4

44/11 = 4

4 = 4

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 5. (2y + 5)/(y + 4) = 1

Solution:

Given:

(2y + 5) / (y + 4) = 1

After cross-multiplication we will get,

2y + 5 = y + 4

2y – y = 4 – 5

y = -1

Now verify the given equation by substituting y = -1



(2y + 5) / (y + 4) = 1

y = -1

(2(-1) + 5) / (-1 + 4) = 1

(-2+5) / 3 = 1

3/3 = 1

1 = 1

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 6. (2x + 1)/(3x – 2) = 5/9

Solution:

Given:

(2x + 1) / (3x – 2) = 5/9

After cross-multiplication we will get,

9(2x + 1) = 5(3x – 2)

18x + 9 = 15x – 10

18x – 15x = -10 – 9

3x = -19

x = -19/3

Now verify the given equation byt substituting x = -19/3

(2x + 1) / (3x – 2) = 5/9

x = -19/3

(2(-19/3) + 1) / (3(-19/3) – 2) = 5/9

(-38/3 + 1) / (-57/3 – 2) = 5/9

(-38 + 3)/3 / (-57 – 6)/3 = 5/9

-35/3 / -63/3 = 5/9

-35/3 × 3/-63 = 5/9

-35/-63 = 5/9

5/9 = 5/9

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 7. (1 – 9y)/(19 – 3y) = 5/8

Solution:

Given:

(1 – 9y) / (19 – 3y) = 5/8

After cross-multiplication we  willget,

8(1- 9y) = 5(19-3y)

8 – 72y = 95 – 15y

8 – 95 = 72y – 15y

57y = -87

y = -87/57

y = -29/19

Now verify the given equation by substituting y = -29/19

(1 – 9y) / (19 – 3y) = 5/8

y = -29/19

(1 – 9(-29/19)) / (19 – 3(-29/19)) = 5/8

(19+261)/19 / (361+87)/19 = 5/8

280/19 × 19/448 = 5/8

280/ 448 = 5/8

5/8 = 5/8

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 8. 2x/(3x + 1) = 1

Solution:



Given:

2x / (3x + 1) = 1

After cross-multiplication we will get,

2x = 1(3x + 1)

2x = 3x + 1

2x – 3x = 1

-x = 1

x = -1

Now verify the given equation by substituting x = -1

2x / (3x + 1) = 1

x = -1

2(-1) / (3(-1) + 1) = 1

-2 /(-3+1) = 1

-2/-2 = 1

1 = 1

Here, L.H.S. = R.H.S.,

Thus the given equation is verified.

Question 9. y – (7 – 8y)/9y – (3 + 4y) = 2/3

Solution:

Given:

y – (7 – 8y)/9y – (3 + 4y) = 2/3

(y – 7 + 8y) / (9y – 3 – 4y) = 2/3

(-7 + 9y) / (5y – 3) = 2/3

After cross-multiplication we will get,

3(-7 + 9y) = 2(5y – 3)

-21 + 27y = 10y – 6

27y – 10y = 21 – 6

17y = 15

y = 15/17

Now verify the given equation by substituting y = 15/17

y – (7 – 8y)/9y – (3 + 4y) = 2/3

y = 15/17

15/17 – (7-8(15/17))/ 9(15/17) – (3 + 4(15/17)) = 2/3

15/17 – (7 – 120/17) / 135/17 – (3 + 60/17) = 2/3

15/17 – ((119-120)/17) / 135/17 – ((51+60)/17) = 2/3

15/17 – (-1/17) / 135/17 – (111/17) = 2/23

((15 + 1)/17) / ((135-111)/17) = 2/3

16/17 / 24/17 = 2/3

16/24 = 2/3

2/3 = 2/3

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Question 10. 6/2x – (3 – 4x) = 2/3

Solution:

Given:

6/ 2x – (3 – 4x) = 2/3

6/(2x – 3 + 4x) = 2/3

6/(6x – 3) = 2/3

After cross-multiplication we will get,

3(6) = 2(6x – 3)

18 = 12x – 6

12x = 18 + 6

12x = 24

x = 24/12

x = 2

Now verify the given equation by substituting x = 2

6/ 2x – (3 – 4x) = 2/3

6/(6x – 3) = 2/3

x = 2

6/ (6(2) – 3) = 2/3

6/(12-3) = 2/3

6/9 = 2/3

2/3 = 2/3

Here, L.H.S. = R.H.S.,

Thus the given equation is verified.

Question 11. 2/3x – 3/2x = 1/12

Solution:

Given:

2/3x – 3/2x = 1/12

By taking LCM for 2 and 3 which is 6

4-9/6x = 1/12

-5/6x = 1/12

After cross-multiplying we will get,



12(-5) = 1 (6x)

-60 = 6x

x = -60/6

x = -10

Now verify the given equation by substituting x = -10

2/3x – 3/2x = 1/12

x = -10

2/3(-10) – 3/2(-10) = 1/12

2/-30 – 3/-20 = 1/12

-4+6/60 = 1/12

5/60 = 1/12

1/12 = 1/12

Here, L.H.S. = R.H.S., 

Thus, the given equation is verified.

Question 12. (3x + 5)/(4x + 2) = (3x + 4)/(4x + 7)

Solution:

Given:

(3x + 5)/ (4x + 2) = (3x + 4)/(4x + 7)

(3x + 5)/ (4x + 2) – (3x + 4)/(4x + 7) = 0

By taking LCM as (4x + 2) (4x + 7)

((3x + 5) (4x + 7) – (3x + 4) (4x + 2)) / (4x + 2) (4x + 7) = 0

After cross-multiplying we will get,

(3x + 5) (4x + 7) – (3x + 4) (4x + 2) = 0

(3x + 5) (4x + 7) – (3x + 4) (4x + 2) = 0

12x2 + 21x + 20x + 35 – 12x2 – 6x – 16x – 8 = 0

19x + 35 – 8 = 0

19x = -27

x = -27/19

Now verify the given equation by substituting, x = -27/19

(3x + 5)/ (4x + 2) = (3x + 4)/(4x + 7)

x = -27/19

(3(-27/19) +5) / (4(-27/19) + 2) = (3(-27/19) + 4) / (4(-27/19) + 7)

(-81/19 + 5) / (-108/19 + 2) = (-81/19 + 4) / (-108/19 + 7)

((-81+95)/19) / ((-108+38)/19) = ((-81+76)/19) / ((-108+133)/19)

14/19 / -70/19 = -5/19 / 25/19

-14/70 = -5/25

-1/5 = -1/5

Here, L.H.S. = R.H.S.,

Thus, the given equation is verified.

Chapter 9 Linear Equation In One Variable – Exercise 9.3 | Set 2




My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!