R00nnYBraiNsbiG
-3|x-2|+10=12
x = 1 and x = 5
x = −1 and x = −5
x = −9 and x = 3
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R00nnYBraiNsbiG
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@AravindG HELP ME PLEASE STEP BY STEP
electrokid
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\[-3|x-2|=2\]
now we square this..
the only way to get rid of the absoute sign is to square it
electrokid
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or make two equations out of it.
R00nnYBraiNsbiG
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ok wait spuare the hole thing
electrokid
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yes see the above simplified orm
electrokid
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\[\left[-3|x-2|\right]^2=2^2\]
R00nnYBraiNsbiG
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ok wat about the + 10
electrokid
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I subtracted it from the two sides
electrokid
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notice that the right side became 12-10=2
R00nnYBraiNsbiG
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where did u get the 12 frm
R00nnYBraiNsbiG
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@electrokid
R00nnYBraiNsbiG
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where did u get the 12 from
electrokid
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\[-3|x-2|+10=12\qquad\text{....given}\\
\qquad\qquad-10\quad-10
\]
R00nnYBraiNsbiG
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ok srry im just learning this ok and then gives u this
[−3|x−2|]^2=2^2
electrokid
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that is ok.
well, this first gives
\[-3|x-2|=2\]
so, we the square it like you just wrote above
R00nnYBraiNsbiG
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yes
electrokid
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\[(-3)^2(x-2)^2=(2^2)\]
notice that the absolute sign has disappeared
R00nnYBraiNsbiG
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so 9*2x-4=4
electrokid
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or to avoid squaring, you can remove the abolute sign in two ways......
\[-3|x-2|=2\implies|x-2|=-{3\over2}\]
R00nnYBraiNsbiG
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how did u get 3/2
electrokid
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my bad... \[\Large{|x-2|=\color{red}{-}{2\over3}}\]
R00nnYBraiNsbiG
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ooh its ok but how did u get that
electrokid
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divide the two sides by "3"
R00nnYBraiNsbiG
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ok
electrokid
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\[{-3|x-2|\over-3}={2\over-3}\]
electrokid
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this gives the above form..
now, by definition of ABSOLUTE value, can it ever become negative?
R00nnYBraiNsbiG
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HEY STOP STOP STOP I WROTE THE PROBLEM DWN WRONG
SRRY
THIS IS THE PROBLEM −3|2x + 6| = −12
electrokid
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ok...
you mean no "10" in there?
R00nnYBraiNsbiG
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yea
electrokid
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this is so much different than what you first asked for
electrokid
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ok.. proceeding similarly, get the absolute quantity on its own...
R00nnYBraiNsbiG
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ik b/c its 2 differnt problems in one
electrokid
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\[\Large{-3|2x-6|=-12\\\text{divide both sides by -3}\\
|2x-6|=4\\\text{to get rid of absolute sign, we get two possible answers}\\\;\\
2x-6=4\qquad{\rm AND}\qquad2x-6=-4\\
2x=4+6\qquad\qquad\qquad2x=-4+6\\
2x=10\qquad\qquad\qquad\quad2x=2\\
\boxed{x=5}\qquad\qquad\qquad\quad\boxed{x=1}}
\]
electrokid
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check, plug in "x=" those numbers in the given problem on the left side. That should give you the right side.
R00nnYBraiNsbiG
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thanks
electrokid
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did you understand?
R00nnYBraiNsbiG
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yes