How do you solve #abs(1/3x - 3) = 9#?

1 Answer
May 7, 2018

#x=-18" or "x=36#

Explanation:

#"the expression inside the absolute value bars can be"#
#"positive or negative leading to 2 possible solutions"#

#1/3x-3=9larrcolor(magenta)"positive value"#

#"add 3 to both sides"#

#rArr1/3x=9+3=12#

#"multiply both sides by 3"#

#rArrx=3xx12=36#

#-(1/3x-3)=9larrcolor(magenta)"negative value"#

#rArr-1/3x+3=9#

#"subtract 3 from both sides"#

#rArr-1/3x=9-3=6#

#"multiply both sides by "-3#

#rArrx=6xx-3=-18#

#color(blue)"As a check"#

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#x=36to|12-3|=|9|=9#

#x=-18to|-6-3|=|-9|=9#

#rArrx=-18" or "x=36" are the solutions"#