-3|x-2|+10=12 x = 1 and x = 5 x = −1 and x = −5 x = −9 and x = 3 No Solution

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-3|x-2|+10=12 x = 1 and x = 5 x = −1 and x = −5 x = −9 and x = 3 No Solution

Mathematics
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@AravindG HELP ME PLEASE STEP BY STEP
\[-3|x-2|=2\] now we square this.. the only way to get rid of the absoute sign is to square it
or make two equations out of it.

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Other answers:

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

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