Mathematics 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): OpenStudy (anonymous):

not the same 1

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