How do you solve for x: $−2|x − 3| = −12$ ?

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Answer 1 · 2017-01-25T10:29:29

$"The Soln. Set="{-3, 9}.$

$-2|x-3|=-12$

$:. |x-3|=-12/-2=6$

Removing $|...|" sign,"$ we have to consider $2" cases :"$ "

$"Case "1 : (x-3) >0, i.e., x>3.$

In this Case, $because (x-3) >0, |x-3|=x-3," by Defn."$

$:. x-3=6 rArr x=6+3=9," & this "x>3.$

$"Case "2 : (x-3)<0, i.e., x<3.$

$:." by Defn., "|x-3|=-(x-3)=3-x.$

$:. |x-3|=6 rArr 3-x=6 rArr x=3-6=-3, <3.$

The Roots $x=-3,9$ satisfy the given eqn.

$"Hence, the Soln. Set="{-3, 9}.$

Enjoy the Maths.!

How do you solve for x: −2|x − 3| = −12 −2|x − 3| = −12?