How do you solve #abs(15-3x)=12#?

1 Answer
Feb 21, 2017

Answer:

#x=1" or " x=9#

Explanation:

There are 2 solutions to the equation.

#"solving "15-3x=color(red)(+-)12#

#color(blue)"first solution"#

#"solve "15-3x=color(red)(+12)#

subtract 15 from both sides of the equation.

#cancel(15)cancel(-15)-3x=12-15#

#rArr-3x=-3#

divide both sides by - 3

#(cancel(-3) x)/cancel(-3)=(-3)/(-3)#

#rArrx=1#

#color(blue)"second solution"#

#"solve "15-3x=color(red)(-12)#

#rArr-3x=-12-15=-27#

#rArrx=(-27)/(-3)=9#

#color(magenta)"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=1to|15-(3xx1)|=|12|=12larr" true"#

#• x=9 to|15-(3xx9)|=|-12|=12larr" true"#

#rArr" solutions are "x=1" or "x=9#