Thursday, April 13, 2017

algebra precalculus - Equation solving, why does this simplification work?



1543.2x=661.6x



How can that equation be simplified as such? :



154(1.6x)=66(3.2x)




Can someone explain?


Answer



Apart from the fact that, as long as denominators are not zero, the formal definition of fractions is that the two equations are equivalent, we have:
1543.2x=661.6x1543.2x(1.6x)=661.6x(1.6x)1543.2x(1.6x)=66(1.6x)(1.6x)1543.2x(1.6x)=661543.2x(1.6x)(3.2x)=66(3.2x)154(3.2x)(1.6x)(3.2x)=66(3.2x)154(1.6x)=66(3.2x)
where all the red parts cancel eachother.


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