How do you solve #abs(5x)+5=45#?

1 Answer
Feb 1, 2017

Answer:

#x++-8#

Explanation:

#"equations involving the" color(blue)" absolute value"# have 2 possible solutions.

Isolate the absolute value.

subtract 5 from both sides of the equation.

#|5x|cancel(+5)cancel(-5)=45-5#

#rArr|5x|=40#

The 2 solutions are obtained by solving #5x=color(red)(+-)40#

#color(blue)"Solution 1"#

#"solve "5x=40rArrx=8#

#color(blue)"Solution 2"#

#"solve "5x=-40rArrx=-8#

#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=8to|5xx8|+5=|40|+5=40+5 =45 color(white)(xx) ✔︎#

#x=-8to|5xx-8|+5=|-40|+5=40+5=45#

#rArrx=+-8" are the solutions"#