How do you solve for x: #−5|3x − 2| = −15#?

1 Answer
Jim G.
May 10, 2017

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

Explanation:

#color(blue)"Isolate " |3x-5|" by dividing both sides by - 5"#

#cancel(-5)/cancel(-5)|3x-2|=(-15)/(-5)#

#rArr|3x-2|=3#

#"the expression inside the bars can be positive or negative"#

#"hence there are 2 possible solutions"#

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

#color(blue)"First solution"#

#3x-2=3#

#"add 2 to both sides"#

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

#rArr3x=5#

#"divide both sides by 3"#

#(cancel(3) x)/cancel(3)=5/3#

#rArrx=5/3#

#color(blue)"Second solution"#

#-(3x-2)=3#

#rArr-3x+2=3#

#"subtract 2 from both sides"#

#rArr-3x=1#

#"divide both sides by - 3"#

#rArrx=-1/3#

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