However You Solve It ...
A Wonderful Equation
Let's solve the following equation
(1) 

Probably the simplest way to approach solving this equation is to multiply both sides by 14 = 7·2. This leads to
10(2x  6) = 21(4x  12).
Multiply through:
20x  60 = 84x  252.
Add 20x and then 252 to both sides:
64x = 192.
Finallly, divide by 62 to obtain x = 192/64 = 3.
Ed Barbeau mentions a professor one of whose students multiplied both sides by 2 and forgot the 7, a second multiplied both sides by 7 and forgot the 2, and a third neglected both the 7 and the 2. All got correct answers.
For example, let's assume we forgot to multiply by 2:
5(2x  6)  = 21(4x  12).  
10x  30  = 84x  252.  
74x  = 222.  
x  = 222/74 = 3. 
Just as before. How come?
References
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