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anonymous

  • 5 years ago

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

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  1. shadowfiend
    • 5 years ago
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    So you have: \[\frac{4}{x} + 7 = \frac{2}{3x}\] We can actually multiply through by \(x\): \[4 = 7x + \frac{2}{3}\]

  2. shadowfiend
    • 5 years ago
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    Er, sorry: \[4 + 7x = \frac{2}{3}\]

  3. shadowfiend
    • 5 years ago
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    Can you solve that equation a little more easily?

  4. anonymous
    • 5 years ago
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    Thank you so much...giving that a try.

  5. shadowfiend
    • 5 years ago
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    Cool :)

  6. anonymous
    • 5 years ago
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    I got -10/21

  7. anonymous
    • 5 years ago
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    but that's not right...what am I doing wrong?

  8. shadowfiend
    • 5 years ago
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    That is right!

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

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

  11. anonymous
    • 5 years ago
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    must have plugged it in wrong....thanks so much! I may be back : )

  12. shadowfiend
    • 5 years ago
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    Awesome! :)

  13. anonymous
    • 5 years ago
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    Hey, Do you think you could help with one more?

  14. anonymous
    • 5 years ago
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    1/x - 5/x^2 = 8/5x

  15. shadowfiend
    • 5 years ago
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    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?

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

  17. shadowfiend
    • 5 years ago
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    That's okay :) Yes, that's right. So what would that make the equation look like?

  18. anonymous
    • 5 years ago
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    x-5 = 8x/5

  19. shadowfiend
    • 5 years ago
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    Exactly. Do you think you can solve that one?

  20. anonymous
    • 5 years ago
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    Thanks, I'll try.

  21. shadowfiend
    • 5 years ago
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    Cool :)

  22. anonymous
    • 5 years ago
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    x= -25/3

  23. shadowfiend
    • 5 years ago
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    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.

  24. anonymous
    • 5 years ago
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    shadow can u help me in the question i asked earlier

  25. anonymous
    • 5 years ago
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    not the same 1

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