Question 145585
{{{3x+1/9+2=x-1/4}}}
{{{3x-x=-1/4-1/9-2}}}
You're on the right track. 
Whenever you add or subtract fractions you need to have the same denominator.
The quickest way is to multiply all the denominators together and transform each fraction to a fraction with that denominator.
In this case, the denominators are 4, 9, and 1. 
Their product is 36. 
Now find each fraction represented with denominator of 36.
{{{-1/4=x/36}}}
{{{-1/4=-9/36}}}
and 
{{{-1/9=y/36}}}
{{{-1/9=-4/36}}}
and finally
{{{2=z/36}}}
{{{2=72/36}}}
Now substitute,
{{{2x=-1/4-1/9-2}}}
{{{2x=-9/36-4/36-72/36}}}
{{{2x=(-9-4-72)/36}}}
{{{2x=(-85)/36}}}
{{{x=(-85)/72}}}
You can use your original equation to check if your answer is correct. 
{{{3x+1/9+2=x-1/4}}}
{{{3*(-85/72)+1/9+2=-(85)/72-1/4}}}
{{{(-255/72)+1/9+2=-(85)/72-1/4}}}
{{{(-255/72)+8/72+144/72=-(85)/72-18/72}}}Change all fractions to denominator of 72.
{{{(-255/72)+8/72+144/72=-(85)/72-18/72}}}
{{{(-255+8+144)/72=(-85-18)/72}}}Multiply both sides by 72.
{{{-255+8+144=-85-18}}}
{{{-255+8+144=-85-18}}}
{{{-103=-103}}}
Your answer leads to a true statement.
It's a good answer.