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I have a problem with the absolute value equation below:

Absolute Value Equation

So my doubt is: Shouldn't the answer of the equation be:

-10|x-2| = $\frac{14}{10}$

Then, |x-2| = $\frac {7}{5}$

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No! $$-6|x-2|-9=4|x-2|+5$$ it's $$|x-2|=-\frac{7}{5},$$ which has no solutions.

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  • $\begingroup$ Is it because $-10|x-2|=14$ then, $-1|x-2| = \frac {14}{10}$ and then $|x-2|$ is multiplied by $-1$ ? $\endgroup$ – Mike Sep 2 '17 at 16:04
  • $\begingroup$ @Mike Yes, of course. $\endgroup$ – Michael Rozenberg Sep 2 '17 at 16:05
  • $\begingroup$ Ok. I was just taking the $-10$ to the other side along and changing the signal there, and about the absolute value, I wasn't considering the $-$ signal left, lol. $\endgroup$ – Mike Sep 2 '17 at 16:10
  • $\begingroup$ @Mike You are welcome! $\endgroup$ – Michael Rozenberg Sep 2 '17 at 16:12

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