How do you solve abs(1/3x - 3) = 913x3=9?

1 Answer
May 7, 2018

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

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"13x3=9positive value

"add 3 to both sides"add 3 to both sides

rArr1/3x=9+3=1213x=9+3=12

"multiply both sides by 3"multiply both sides by 3

rArrx=3xx12=36x=3×12=36

-(1/3x-3)=9larrcolor(magenta)"negative value"(13x3)=9negative value

rArr-1/3x+3=913x+3=9

"subtract 3 from both sides"subtract 3 from both sides

rArr-1/3x=9-3=613x=93=6

"multiply both sides by "-3multiply both sides by 3

rArrx=6xx-3=-18x=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|123|=|9|=9

x=-18to|-6-3|=|-9|=9x=18|63|=|9|=9

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