How do you solve #|x - 2| - 2= 7#?

1 Answer
Jim G.
Nov 13, 2016

#x=11,x=-7#

Explanation:

The absolute value gives the measure of how far a value is from the origin.

That is #|4|=4" and " |-4|=4#

as both 4 and - 4 are 4 units from the origin.

Therefore there are 2 equations to be solved here.

Isolate the absolute value on the left side.

add 2 to both sides.

#|x-2|cancel(-2)cancel(+2)=7+2#

#rArr|x-2|=9#

#(1)" solve " x-2=9rArrx=11#

#(2) " solve " -(x-2)=9#

#rArr-x+2=9rArr-x=9-2=7#

#rArrx=-7#

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