1/3(2x+6)-4=6-4/3*x+8
Solve for x:
(2 x+6)/3-4 = 14-(4 x)/3
Put each term in (2 x+6)/3-4 over the common denominator 3: (2 x+6)/3-4 = (2 x+6)/3-(12)/3:
(2 x+6)/3-(12)/3 = 14-(4 x)/3
(2 x+6)/3-(12)/3 = ((2 x+6)-12)/3:
(2 x-12+6)/3 = 14-(4 x)/3
Add like terms. 6-12 = -6:
(2 x-6)/3 = 14-(4 x)/3
Put each term in 14-(4 x)/3 over the common denominator 3: 14-(4 x)/3 = 42/3-(4 x)/3:
(2 x-6)/3 = 42/3-(4 x)/3
42/3-(4 x)/3 = (42-4 x)/3:
(2 x-6)/3 = (42-4 x)/3
Multiply both sides by 3:
2 x-6 = 42-4 x
Add 4 x to both sides:
4 x+2 x-6 = (4 x-4 x)+42
4 x-4 x = 0:
4 x+2 x-6 = 42
2 x+4 x = 6 x:
6 x-6 = 42
Add 6 to both sides:
6 x+(6-6) = 42+6
6-6 = 0:
6 x = 42+6
42+6 = 48:
6 x = 48
Divide both sides of 6 x = 48 by 6:
(6 x)/6 = 48/6
6/6 = 1:
x = 48/6
The gcd of 48 and 6 is 6, so 48/6 = (6×8)/(6×1) = 6/6×8 = 8:
Answer: | x = 8
