What is 2/5x-4=8-3/5x

x = 12

Step-by-step explanation:

Solve for x:

(2 x) / 5 - 4 = 8 - (3 x) / 5

Put each term in (2 x) / 5 - 4 over the common denominator 5: (2 x) / 5 - 4 = (2 x) / 5 - 20/5:

(2 x) / 5 - 20/5 = 8 - (3 x) / 5

(2 x) / 5 - 20/5 = (2 x - 20) / 5:

(2 x - 20) / 5 = 8 - (3 x) / 5

Put each term in 8 - (3 x) / 5 over the common denominator 5: 8 - (3 x) / 5 = 40/5 - (3 x) / 5:

(2 x - 20) / 5 = 40/5 - (3 x) / 5

40/5 - (3 x) / 5 = (40 - 3 x) / 5:

(2 x - 20) / 5 = (40 - 3 x) / 5

Multiply both sides by 5:

2 x - 20 = 40 - 3 x

Add 3 x to both sides:

3 x + 2 x - 20 = (3 x - 3 x) + 40

3 x - 3 x = 0:

3 x + 2 x - 20 = 40

2 x + 3 x = 5 x:

5 x - 20 = 40

Add 20 to both sides:

5 x + (20 - 20) = 20 + 40

20 - 20 = 0:

5 x = 40 + 20

40 + 20 = 60:

5 x = 60

Divide both sides of 5 x = 60 by 5:

(5 x) / 5 = 60/5

5/5 = 1:

x = 60/5

The gcd of 60 and 5 is 5, so 60/5 = (5*12) / (5*1) = 5/5*12 = 12:

Answer: x = 12