## Transformation trouble: 3x + 3/2(2x - 1) = 2

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diaste
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### Transformation trouble: 3x + 3/2(2x - 1) = 2

I keep coming up with the same solution for this problem which differs from the book.

3x + 3/2(2x - 1)= 2
I continue to get 7/15 and the book says it's 7/12. I know this may appear simple but it has me stumped.
First I multiplied by the reciprocal, then I tried distributing. I keep coming up with the same answer but it doesn't check.
What am I doing wrong?

stapel_eliz
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### Re: Transformation trouble: 3x + 3/2(2x - 1) = 2

diaste wrote:3x + 3/2(2x - 1)= 2

As posted, the equation is as follows:

. . . . .$3x\, +\, \frac{3}{2(2x\, -\, 1)}\, =\, 2$

I think you really mean the following:

. . . . .$3x\, +\, \frac{3}{2}\left(2x\, -\, 1\right)\, =\, 2$

I will guess that the instructions were to "solve" or "solve and check"...?

diaste wrote:What am I doing wrong?

Unfortunately, since you didn't show your steps, I'm afraid there's no way to know where you might have made an error. But it's easy to check the book's solution: plug it in and see if it works!

If I have guessed your meaning correctly, this computation would be as follows:

. . . . .$3\left(\frac{7}{12}\right)\, +\, \left(\frac{3}{2}\right)\left[2\left(\frac{7}{12}\right)\, -\, 1\right]$

. . . . .$\left(\frac{3}{1}\right)\left(\frac{7}{12}\right)\, +\, \left(\frac{3}{2}\right) \left[\left(\frac{2}{1}\right)\left(\frac{7}{12}\right)\, -\, 1\right]$

. . . . .$\left(\frac{1}{1}\right)\left(\frac{7}{4}\right)\, +\, \left(\frac{3}{2}\right) \left[\left(\frac{1}{1}\right)\left(\frac{7}{6}\right)\, -\, 1\right]$

. . . . .$\frac{7}{4}\, +\, \left(\frac{3}{2}\right)\left[\frac{7}{6}\, -\, \frac{6}{6}\right]$

. . . . .$\frac{7}{4}\, +\, \left(\frac{3}{2}\right)\left(\frac{1}{6}\right)$

. . . . .$\frac{7}{4}\, +\, \left(\frac{1}{2}\right)\left(\frac{1}{2}\right)$

. . . . .$\frac{7}{4}\, +\,\frac{1}{4}$

. . . . .$\frac{7\, +\,1}{4}\, =\, \frac{8}{4}\, =\, 2$

So the book's solution is indeed correct (assuming I guessed the equation right).

Eliz.

diaste
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Joined: Sat Jan 17, 2009 1:54 pm
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### Re: Transformation trouble: 3x + 3/2(2x - 1) = 2

Elizabeth,
Thanks for the reply and apologies for not getting back sooner.
I figured out what I did wrong in the above equation. I didn't distribute properly. The answer is .58 or 7 divided by 12.
Thanks again!