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Bunuel
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DF14980N
Hello,

I got this question wrong and I'm reviewing my answer and I see why, but I'm stuck at how I'm supposed to calculate the correct answer.

Here is how I calculated:

1/x = 2.5
2.5x = 1
x = 1/2.5 <-- (change this to 2/5)
x = 2/5

And then I do this:

1/(2/5 - 2/3) <-- (change these to denominators of 15)
1/(6/15 - 10/15)
1/(-4/15)

At this point I am confused as to how to proceed next. How would I achieve -15/4?

If \(\frac{1}{x}= 2.5\), then what is the value of \(\frac{1}{x – \frac{2}{3}}\)?

A. 2.25.
B. –3.5.
C. –3.75.
D. 1.75.
E. 3.75.

\(\frac{1}{x}= 2.5\);

\(\frac{1}{x}= \frac{5}{2}\);

\(x = \frac{2}{5}\).

Thus, \(\frac{1}{x – \frac{2}{3}}=\frac{1}{\frac{2}{5} – \frac{2}{3}}=\frac{1}{\frac{6}{15} – \frac{10}{15}}=\frac{1}{-\frac{4}{15}}=-\frac{15}{4}=-3.75\).

Answer: C.
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I see. So to move the 15 into the parent numerator you would simply just flip it up into its position. So 1/(-4/15) is the same as -15/4.
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I see. So to move the 15 into the parent numerator you would simply just flip it up into its position. So 1/(-4/15) is the same as -15/4.

Yes. \(\frac{x}{\frac{a}{b}}=x*\frac{b}{a}\). So, \(\frac{1}{-\frac{4}{15}}=1*(-\frac{15}{4})=-\frac{15}{4}\)
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\(\frac{1}{x}= 2.5\) = \(\frac{5}{2}\)
=> x = \(\frac{2}{5}\)

=> \(\frac{1}{x – \frac{2}{3}}\)
= 1 / ((2/5) - (2/3))
= 1 / ((2*3 - 2*5) / 15)
= \(\frac{15}{-4}\)
= - 3.75

So, Answer will be C
Hope it helps!
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Bunuel
If \(\frac{1}{x}= 2.5\), then what is the value of \(\frac{1}{x – \frac{2}{3}}\)?

A. 2.25.
B. –3.5.
C. –3.75.
D. 1.75.
E. 3.75.
x = 4/10

So, \(x – \frac{2}{3}\)

Or, \(\frac{4}{10} - \frac{2}{3}=\frac{-4}{15}\)

So, \(\frac{1}{x – \frac{2}{3}}= -\frac{15}{4 }= -3.75\), Answer will be (C)
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