How do you solve the equation #abs(5-6x)=7#?

1 Answer
May 30, 2017

Answer:

#x=-1/3" or "x=2#

Explanation:

#"the expression inside the absolute value can be positive or"#
#"negative"#

#rArr5-6x=color(red)(+-)7#

#color(blue)"first solution"#

#5-6x=color(red)(+)7#

#"subtract 5 from both sides"#

#rArr-6x=2#

#"divide both sides by - 6"#

#rArrx=2/(-6)=-1/3#

#color(blue)"second solution"#

#5-6x=color(red)(-)7#

#"subtract 5 from both sides"#

#rArr-6x=-12#

#"divide both sides by - 6"#

#rArrx=(-12)/(-6)=2#

#color(blue)"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=-1/3to|5+2|=|7|=7#

#x=2to|5-12|=|-7|=7#

#rArrx=-1/3" or "x=2" are the solutions"#