How do you solve #abs(2x - 6) = 12#?

2 Answers
Apr 8, 2018

#x=-3, 9#

Explanation:

#2x-6=12 and 2x-6=-12#

#2x=18 and 2x=-6#

#x=9 and x=-3#

Apr 8, 2018

#x=-3" or "x=9#

Explanation:

#"the expression inside the absolute value can be positive"#
#"or negative, thus there are 2 possible solutions"#

#color(magenta)"Positive value"#

#2x-6=12#

#"add 6 to both sides"#

#rArr2x=18rArrx=9#

#color(magenta)"Negative value"#

#-(2x-6)=12#

#rArr-2x+6=12#

#"subtract 6 from both sides"#

#rArr-2x=6#

#"divide both sides by "-2#

#rArrx=-3#

#color(blue)"As a check"#

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

#|(2xx9)-6|=|18-6|=|12|=12#

#|(2xx-3)-6|=|-6-6|=|-12|=12#

#rArrx=-3" or "x=9" are the solutions"#