How do you solve #|2x - 3| = |x + 2| #?

1 Answer
Apr 8, 2017

Answer:

#x=1/3" or " x=5#

Explanation:

There are 2 possible solutions to the equation.

#2x-3=color(red)(+-)(x+2)#

#color(blue)"first solution"#

#2x-3=x+2#

#"subtract x from both sides."#

#2x-x-3=cancel(x)cancel(-x)+2#

#rArrx-3=2#

#"add 3 to both sides."#

#xcancel(-3)cancel(+3)=2+3#

#rArrx=5#

#color(blue)"second solution"#

#2x-3=-x-2#

#rArr3x=1#

#rArr x=1/3#

#color(blue)"As a check"#

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

#"left side "=|(2xx5)-3|=|7|=7#

#"right side "=|5+2|=|7|=7#

#"left side "=|2/3-3|=|-2 1/3|=2 1/3#

#"right side "=|1/3+2|=|2 1/3|=2 1/3#

#rArrx=1/3" or " x=5" are the solutions"#