SOLVING EQUIVALENT FRACTIONS WITH VARIABLES

Solve for x :

Problem 1 :

Solution :

x/2 = 4/7

Since we have only fractions on both sides of the equal sign, we can do the cross multiplication.

7x = 4(2)

7x = 8

Dividing by 7 on both sides

x = 8/7

So, the value of x is 8/7.

Problem 2 :

Solution :

Using cross product rule,

3x = 2(x - 2)

3x = 2x - 4

Subtracting 2x on both sides

3x - 2x = -4

x = -4

So, the value of x is -4.

Problem 3 :

Solution :

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

Using distributive property, we get

4x + 4 = 6x - 3

Subtracting 6x on both sides

4x - 6x + 4 = -3

Subtracting 4 on both sides

-2x + 4 = -3

-2x = -3 - 4

-2x = -7

Dividing by -2 on both sides

x = 7/2

So, the value of x is 7/2.

Problem 4 :

Solution :

2(2x) = 3(5 - x)

4x = 15 - 3x

Adding 3x on both sides

4x + 3x = 15

7x = 15

Dividing by 7 on both sides

x = 15/7

So, the value of x is 15/7.

Problem 5 :

Solution :

Doing cross multiplication, we get

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

6x + 4 = 10x - 5

Subtracting 10 on both sides

6x - 10x + 4 = -5

-4x + 4 = -5

Subtracting 4 on both sides

-4x = - 5 - 4

-4x = -9

Dividing by -4 on both sides

x = 9/4

Problem 6 :

Solution :

(2x - 1)/3 = (4 - x)/6

6(2x - 1) = 3(4 - x)

12x - 6 = 12 - 3x

12x + 3x = 12 + 6

15x = 18

x = 18/15

x = 6/5

So, the solution is 6/5.

Problem 7 :

Solution :

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

8x + 14 = 35 - 7x

8x + 7x = 35 - 14

15x = 21

x = 21/15

x = 7/5

So, the solution is 7/5.

Problem 8 :

Solution :

-2(3x + 1) = 6(4x - 1)

-6x - 2 = 24x - 6

-6x - 24x = -6 + 2

-30x = -4

x = 4/30

x = 2/15

So, the solution is 2/15.