SOLUTION: r-5/2=r+2/3

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Question 229030: r-5/2=r+2/3
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
%28r-5%29%2F2=%28r%2B2%29%2F3

There are two ways of thinking of this, and both give the same result.

Method I: Multiply both sides of the equation by the LCD which is 6.
+6%2A%28%28r-5%29%2F2%29=+6%2A%28%28r%2B2%29%2F3%29+
3%28r-5%29+=+2%28r%2B2%29
3r-15=+2r%2B4

Subtract 2r from each side:
3r-2r-15=+2r-2r%2B4
r-15=+4

Add +15 to each side:
r=+19

Check: %28r-5%29%2F2=%28r%2B2%29%2F3
%2819-5%29%2F2=%2819%2B2%29%2F3
14%2F2=21%2F3
7=7 IT CHECKS!!

METHOD II:
a%2Fb=c%2Fd means that ad=bc

Likewise:
%28r-5%29%2F2=%28r%2B2%29%2F3 means that 3%28r-5%29=2%28r%2B2%29+

Notice that this is EXACTLY the equation you had to solve in Method I, so this is exactly the same result. That's the way with math! No matter how you do it, as long as you don't BREAK the rules or make careless errors, you always get the same result!! Which way do you like best???

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus