Question 766050
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Simple sign mistake.  You said:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-10}{30}\ +\ \frac{a}{30}\ =\ -1]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-1}{3}\ +\ \frac{a}{30}\ =\ -1]

which was all ok, but then you said:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-1}{3}\ +\ 1\ =\ \frac{a}{30}]

But you should have said:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-1}{3}\ +\ 1\ =\ -\frac{a}{30}]

And you will find that it works out to the correct answer from here.

Having said that, I'd like to point out that you did a great deal of extra work.

Start over from the beginning:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-10\,+\,a}{30}\ =\ -1]

But this time as a first step, multiply both sides by 30:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -10\ +\ a\ =\ -30]

Then just add 10 to both sides:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ -20]

as expected.

Lesson:  Things usually get simpler if you can find a multiplier that gets rid of all your denominators.

John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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