Your problem is when distributing the LCD.
6(3x) = 18x
You don't put (18)(6x) = 72x
According to my book, and some sources I've found on the internet, the common strategy for solving a linear equation is:
1) If fractions are present, multiply each side by the LCD to eliminate them. If decimals are present, multiply each side by a power of 10 to eliminate them.
2) Use the distributive property to remove parentheses.
3) Combine any like terms.
4) Use the addition property of equality to get all variables on one side and numbers on the other.
5) Use the multiplication property of equality to get a single variable on one side.
6) Check by replacing the variable in the original equation with your solution.
My problem is 1) and 2). I've learned the hard way that if you multiply each side by the LCD before distributing to any fractions within parentheses, you get the wrong answer.
Attached is my wrong answer with work shown. To come up with the right answer, at step 1 I needed to distribute the 1/2 and 1/3 to the parenthesis first.
Is there any reason to not do step 2 in the strategy as a general rule before step 1? Why would they be in that order if it sometimes does not work?