Question 58037
Hi Karen,
Your solution is right, so I'm going to show you the checking part.

(5x+3) / (3x)= (7 / 3) - (9 / x)

I tried multiplying (7 / 3)(x / x) and (9 / x)(3 / 3) to get the right side to become:
(7x-27) / (3x) but then I thought I could just get rid of the denominators since they were the same and I'd be left with (5x+3) = (7x-27), which eventually gives an answer of 15.  
{{{(7(15)-27)/(3(15))=(7/3)-9/15}}}
{{{(105-27)/45=7*5/(3*5)-9/15}}}
{{{78/45=35/15-9/15}}}
{{{3*26/(3*15)=(35-9)/15}}}
{{{26/15=26/15}}}  You're right.
Checking this kind of problem is a bear, unless you reduce both sides completely, you won't know both sides are equal.  I usually like to check these things by storing values into my graphing calculator.  Which gave me 1.7333...=1.7333... proving you were right.
Happy Calculating, Karen!!!