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Mathematics
OpenStudy (anonymous):

|3x|+8=9

OpenStudy (anonymous):

\[|3x|=9-8=1\] \[|x|=\frac{1}{3}\] \[x=\frac{1}{3} \text{ or } x=\frac{-1}{3}\]

OpenStudy (anonymous):

got it ! :)

OpenStudy (anonymous):

^ The answer is correct but |x| does not equal 1/3.. It is |3x| = 1 3x = 1 or 3x = -1 x= 1/3 or x = -1/3

jimthompson5910 (jim_thompson5910):

you have the right answer, but the second step is a bit incorrect

jimthompson5910 (jim_thompson5910):

yeah denebel has it right

OpenStudy (anonymous):

so its 1/3, -1/3

OpenStudy (anonymous):

Yes

OpenStudy (anonymous):

well actually if \[|3x|=1\] the \[|x|=\frac{1}{3}\] is correct

OpenStudy (anonymous):

Check the properties of the absolute values: http://en.wikipedia.org/wiki/Absolute_value Specially the Multiplicativeness property. What I did is correct since we know that the value of the coefficient is positive. I don't mean to contradict you guys, but I've got a PhD and am pretty sure what i did is correct.

OpenStudy (anonymous):

yes it is correct, since we know \[|3x|=|3||x|=3|x|\]

OpenStudy (anonymous):

but the answer is 1/3 or -1/3?

OpenStudy (anonymous):

as we say on who wants to be a millionaire the "final answer" is \[x=\frac{1}{3}\] or \[x=-\frac{1}{3}\]

jimthompson5910 (jim_thompson5910):

just type 1/3,-1/3 and you'll be fine

OpenStudy (anonymous):

why does the absolute value of x=1/3?

OpenStudy (anonymous):

ok, so im good.

OpenStudy (anonymous):

because \[|ab|=|a||b|\] and since \[|3x|=|3||x|=3|x|=1\] we know that \[|x|=\frac{1}{3}\]

OpenStudy (anonymous):

very clear answer thanks

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