SOLVE EQUATIONS WITH VARIABLES IN THE DENOMINATOR AND NUMERATOR

Solve the equation:

Problem 1 :

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

Solution : 

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

Multiply by (2x + 7) on both sides.

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

3x + 5 = 10x + 35

10x - 3x = -35 + 5

7x = -30

x = -30/7

Problem 2 :

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

Solution :

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

Multiply by (y + 4) on both sides.

2y + 5 = y + 4

2y - y = 4 - 5

y = -1

Problem 3 :

(5z - 3)/2z = 8/9

Solution :

(5z - 3) / 2z = 8/9

9(5z - 3) = 8(2z)

45z - 27 = 16z

45z - 16z = 27

29z = 27

z = 27/29

Problem 4 :

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

Solution :

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

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

8 - 72y = 95 - 15y

-72y + 15y = 95 - 8

-57y = 87

y = - 87/57

y = - 29/19

Problem 5 :

(0.4z - 3) / (1.5z + 9) = -7/5

Solution :

(0.4z - 3) / (1.5z + 9) = -7/5

5(0.4z - 3) = -7(1.5z + 9)

2z - 15 = -10.5z - 63

2z + 10.5z = - 63 + 15

12.5z = - 48

z = -48/12.5

z = -3.84

Problem 6 :

(5y - 3) / (2y + 1) = 2/5

Solution :

(5y - 3) / (2y + 1) = 2/5

5(5y - 3) = 2(2y + 1)

25y - 15 = 4y + 2

25y - 4y = 2 + 15

21y = 17

y = 17/21

Problem 7 :

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

Solution :

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

2x = -3(3x + 1)

2x = -9x - 3

2x + 9x = -3

11x = -3

x = -3/11

Problem 8 :

[17(2 - x) - 5(x + 12)]/(1 - 7x) = 8

Solution :

17(2 - x) - 5(x + 12)/1 - 7x = 8

17(2 - x) - 5(x + 12) = 8(1 - 7x)

34 - 17x - 5x - 60 = 8 - 56x

-17x - 5x + 56x = -34 + 60 + 8

34x = 34

x = 34/34

x = 1