Math CentralQuandaries & Queries


Question from Amber:

Um i am wondering what this equation equals. Thank you for your time and help.



Hi Amber,

The first thing to notice is that both sides of this equation are divisible by 2 and thus dividing each side by 2 yields

\[xy = x \times 2 y = 2xy.\]

Each side of this equation is a multiple of $x$ so it looks like you can divide each side by $x.$ But if $x$ is zero you know you can't divide by zero. So what if $x = 0?$ In this case the equation $xy = 2xy$ is true and hence $x = 0$ is a solution of the equation.

What if $x \neq 0?$ If this is true you can divide both sides of $xy = 2xy$ by $x.$ What is the solution of the remaining equation?

I hope this helps,

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