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.!