How do you solve abs(1/3x - 3) = 9?
1 Answer
May 7, 2018
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"