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anonymous

  • one year ago

What is the value of x in the proportion. x/2=16x-3/20 1. 2 2. -3/2 3. 1/4 4. 1/2

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  1. whpalmer4
    • one year ago
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    \[\frac{x}{2} = \frac{16x-3}{20}\] is that how the problem reads?

  2. anonymous
    • one year ago
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    yes

  3. whpalmer4
    • one year ago
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    Do you know about cross-multiplication?

  4. anonymous
    • one year ago
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    yes

  5. whpalmer4
    • one year ago
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    Good. Cross-multiply and solve the resulting equation for \(x\)

  6. anonymous
    • one year ago
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    actually i am confused on how to cross multiply on this can you explain?

  7. whpalmer4
    • one year ago
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    Okay, \[\frac{x}{2} = \frac{16x-3}{20}\] multiply the numerator of one by the denominator of the other \[x*20 = 2*(16x-3)\]\[20x = 32x - 6\]

  8. whpalmer4
    • one year ago
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    What you are effectively doing is making a common denominator of 1

  9. whpalmer4
    • one year ago
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    Can you solve \[20x = 32x - 6\] for \(x\)?

  10. anonymous
    • one year ago
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    x=1/2

  11. whpalmer4
    • one year ago
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    let's try it in the original equation and make sure it works: \[\frac{\frac{1}{2}}{2} = \frac{16(\frac{1}{2})-3}{20}\]\[\frac{1}{4} = \frac{8-3}{20}\]\[\frac{1}{4} = \frac{5}{20} = \frac{1}{4}\checkmark\]

  12. anonymous
    • one year ago
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    Okay i get it now thanks!

  13. anonymous
    • one year ago
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    Can you help me with one more?

  14. whpalmer4
    • one year ago
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    We could also solve like this: \[\frac{x}{2} = \frac{16x-3}{20}\]Multiply both sides by 20\[20*\frac{x}{2} = 20*\frac{16x-3}{20}\]\[10x = 16x-3\]\[10x-10x+3 = 16x-10x+3-3\]\[3=6x\]\[x=\frac{1}{2}\]

  15. anonymous
    • one year ago
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    Wait so 1/2 is the answer or 1/4?

  16. whpalmer4
    • one year ago
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    the answer is x = 1/2. what I did was plug the value we got for x back into the original equation to make sure that it made a true statement. Let's say that I made a mistake somewhere and decided that \(x=2\) is the right answer. Well, when I plug that back into the original, I get: \[\frac{2}{2} = \frac{16(2)-3}{20}\]\[1 = \frac{29}{20}\]and that is not true, so that means that \(x=2\) is NOT the correct answer.

  17. anonymous
    • one year ago
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    Ohhh okay thank you so much. I am gonna open another question can you help me?

  18. whpalmer4
    • one year ago
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    sure, just "tag" me by putting "@whpalmer4" in a response and I'll get a notification

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