Answer:
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
