<PRE><B>Question 83329</B>
The goal of solving for a variable is to isolate the variable


{{{12r-18=13r+18}}} Start with the given equation


{{{12r+cross(-18+18)=13r+18+18}}} Add 18 to both sides


{{{12r-13r=cross(13r-13r)+36}}} Subtract 13r from both sides


{{{-1(-r)=-1(36)}}} Multiply both sides by -1 to make r positive 


So we get the answer


{{{r=-36}}} 



Check:

{{{12(-36)-18=13(-36)+18}}}


{{{-432-18=-468+18}}}


{{{-450=-450}}} works. This verifies our answer.</PRE>