Question

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Why did (x - 2) stay? How come 5 was divided by 30 and not 28? (If we plug in the LCM, 30, into x - 2, we get 28, so it should have been 28/5, right? But that's not the case. Explain please :)

Answer 1

you are not plugging the least common multiple in to anything
you are multiplying by it

Answer 2

Multiplying it? I thought we are taking the LCM, putting it in the numerator (the x terms, in it's place) then dividing it by the denominator to clear it

Answer 3

\[\frac{x-2}{5}+\frac{x}{3}=\frac{x}{2}\]\[30\times \left(\frac{x-2}{5}+\frac{x}{3}\right)=\frac{x}{2}\times 30\]

Answer 4

on the right you get \(15x\)

Answer 5

on the left you get
\[6(x-2)+10x\]

Answer 6

On the right - I don't understand how we still have x - 2. Why don't we save

30x - 60/5, if we multiplied it? Can you give some insight on the multiplication process that took place here.

Answer 7

why are you multiplying by 30 to begin with? instead of say 15 or 100?

Answer 8

Well, because 30 is the LCM, right?

Answer 9

which means what exactly?

Answer 10

It's the least common multiple of the two. Multiplying the numerator by 30, then divide it, helps keep the proportions equal, I suppose. I don't have much insight; this is just what my instructor told me. This is how we clear fractions.

Answer 11

least common multiple means each of your denominators divides the lcm evenly
that is why you will have no fractions when you are done
siince 5 goes in to 30 6 times you have
\[30\times \left(\frac{x-2}{5}\right)\]
\[\cancel{30}^6\times \left(\frac{x-2}{\cancel5}\right)=6\times (x-2)\]
\[

Answer 12

Ah, that makes more sense. Now that I understand that, can you tell me why we didn't do anything with (x - 2). How come it sits idle by and doesn't also get multiplied by 30?