1/6 - x/2 = x -5/3

The x term on the right... can you convert it to an equivalent fraction over 2?

I don't know how to do that.

\[\frac{1}{6}+\bigg (-\frac{1}{6} \bigg) +\frac{-x}{2}=\frac {x}{1} + \frac {-5}{3}+\bigg (-\frac{1}{6} \bigg)\]

Bring the 1/6 over to the left. Also, Make the x on the right a fraction (every number is a fraction over one).

Now, can you show me how it's done?

Ok, from the equation above, we now have... \[\frac{-x}{2}=\frac {x}{1} + \frac {-5}{3}+\bigg (-\frac{1}{6} \bigg) \Rightarrow \] \[\frac{-x}{2}=\frac {x}{1} + \frac {-10}{6}+\bigg (-\frac{1}{6} \bigg ) \Rightarrow \frac{-x}{2}=\frac {x}{1} + \frac {-9}{6}\]

Any questions so far? I had to double the top and bottom of -5/3 so I could add it to -1/6. Oooops.. Just spotted a math error should be... \[\frac{-x}{2}=\frac {x}{1} + \frac {-10}{6}+\bigg (-\frac{1}{6} \bigg ) \Rightarrow \frac{-x}{2}=\frac {x}{1} + \frac {-11}{6}\]

Are you following so far? If so, what is the next step????

Well, I'm just writing down the way that you've done it.So, what's the answer?

OK - now you can get rid of the fractions. 6 is the biggest denominator and every other denoninator divides into it. Can you multiply both sides through by 6?

I mean, I know how to multiply the bottom part,but, the top part is confusing.

OK, so we will multiply each term by 6/1, canceling top and bottom as we go. It will take me a while to format this so try on your own while I'm typing. OK. :-)

\[\frac{6}{1}*\frac{-x}{2}=\frac{6}{1}*\frac {x}{1} + \frac {-11}{6}*\frac{6}{1}\] OK. next we need to cancel (we're using common factors - but I won't show that step I'll just do it.

\[-3x=6x+(-11)\] Now the fractions are eliminated. Making sense (check all my math).

That part was kind of crucial so tell me if any of that confused you.

Yes, it was, and, I'm still not following you.

I mean, all I really need is the answer.

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