Question

What is the solution to the equation 1/3(x-2)=1/5(x+4)+2

Answer 1

1/3(x-2) = 1/5(x + 4) + 2 --- distribute through the parenthesis
1/3x - 2/3 = 1/5x + 4/5 + 2 --- lets get rid of the fractions by multiplying everything by the common denominator, which is 15.
giving us :
5x - 10 = 3x + 12 + 30 -- combine what terms you can
5x - 10 = 3x + 42 -- subtract 3x from both sides
5x - 3x - 10 = 42 -- add 10 to both sides
5x - 3x = 42 + 10 -- combine like terms
2x = 52 -- divide both sides by 2
x = 26

check..
1/3(26 - 2) = 1/5(26 + 4) + 2
1/3(24) = 1/5(30) + 2
24/3 = 30/5 + 2
8 = 6 + 2
8 = 8 (correct)

SOLUTION : x = 26