How do you solve abs(1/3x - 3) = 9∣∣∣13x−3∣∣∣=9?
1 Answer
Explanation:
"the expression inside the absolute value bars can be"the expression inside the absolute value bars can be
"positive or negative leading to 2 possible solutions"positive or negative leading to 2 possible solutions
1/3x-3=9larrcolor(magenta)"positive value"13x−3=9←positive value
"add 3 to both sides"add 3 to both sides
rArr1/3x=9+3=12⇒13x=9+3=12
"multiply both sides by 3"multiply both sides by 3
rArrx=3xx12=36⇒x=3×12=36
-(1/3x-3)=9larrcolor(magenta)"negative value"−(13x−3)=9←negative value
rArr-1/3x+3=9⇒−13x+3=9
"subtract 3 from both sides"subtract 3 from both sides
rArr-1/3x=9-3=6⇒−13x=9−3=6
"multiply both sides by "-3multiply both sides by −3
rArrx=6xx-3=-18⇒x=6×−3=−18
color(blue)"As a check"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|=9x=36→|12−3|=|9|=9
x=-18to|-6-3|=|-9|=9x=−18→|−6−3|=|−9|=9
rArrx=-18" or "x=36" are the solutions"⇒x=−18 or x=36 are the solutions
