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OpenStudy (anonymous):

Can anyone help with this one 4/x +7 = 2/3x Thank you!!

OpenStudy (shadowfiend):

So you have: \[\frac{4}{x} + 7 = \frac{2}{3x}\] We can actually multiply through by \(x\): \[4 = 7x + \frac{2}{3}\]

OpenStudy (shadowfiend):

Er, sorry: \[4 + 7x = \frac{2}{3}\]

OpenStudy (shadowfiend):

Can you solve that equation a little more easily?

OpenStudy (anonymous):

Thank you so much...giving that a try.

OpenStudy (shadowfiend):

Cool :)

OpenStudy (anonymous):

I got -10/21

OpenStudy (anonymous):

but that's not right...what am I doing wrong?

OpenStudy (shadowfiend):

That is right!

OpenStudy (shadowfiend):

Try plugging back into the original equation: \[\begin{align} \frac{4}{\frac{-10/21}} + 7 &= \frac{2}{3\frac{-10}{21}}\\ \frac{4\cdot 21}{-10} + 7 &= \frac{2\cdot 21}{-30}\\ \frac{84}{-10} + \frac{70}{10} &= \frac{42}{-30}\\ \frac{-84 + 70}{10} &= \frac{-14}{10}\\ \frac{-14}{10} &= \frac{-14}{10} \end{align}\]

OpenStudy (shadowfiend):

Whoops. Sorry about that. \[\begin{align} \frac{4}{\frac{-10}{21}} + 7 &= \frac{2}{3\frac{-10}{21}}\\ \frac{4\cdot 21}{-10} + 7 &= \frac{2\cdot 21}{-30}\\ \frac{84}{-10} + \frac{70}{10} &= \frac{42}{-30}\\ \frac{-84 + 70}{10} &= \frac{-14}{10}\\ \frac{-14}{10} &= \frac{-14}{10} \end{align}\]

OpenStudy (anonymous):

must have plugged it in wrong....thanks so much! I may be back : )

OpenStudy (shadowfiend):

Awesome! :)

OpenStudy (anonymous):

Hey, Do you think you could help with one more?

OpenStudy (anonymous):

1/x - 5/x^2 = 8/5x

OpenStudy (shadowfiend):

Ok, so generally you want to multiply by the greatest power in a denominator so that you can have no \(x\) in the denominators. What is that in this case?

OpenStudy (anonymous):

Thanks. Sorry, Im multi-tasking so I keep walking away. So multiply by \[x^{2}\] ?

OpenStudy (shadowfiend):

That's okay :) Yes, that's right. So what would that make the equation look like?

OpenStudy (anonymous):

x-5 = 8x/5

OpenStudy (shadowfiend):

Exactly. Do you think you can solve that one?

OpenStudy (anonymous):

Thanks, I'll try.

OpenStudy (shadowfiend):

Cool :)

OpenStudy (anonymous):

x= -25/3

OpenStudy (shadowfiend):

That's what I got too :) Remember to double-check it by plugging it into the original equation and making sure the equality holds true.

OpenStudy (anonymous):

shadow can u help me in the question i asked earlier

OpenStudy (anonymous):

not the same 1

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