How do you solve #|x + 5| = 9#?

2 Answers
Narad T.
Apr 22, 2018

The solutions are #S={4, -14}#

Explanation:

To solve equation with absolute values, procced as follows :

#{(|x+5|=9) : }#

#<=>#, #{(x+5=9),(-x-5=9):}#

#<=>#, #{(x=9-5),(x=-5-9):}#

#<=>#, #{(x=4),(x=-14):}#

The solutions are #S={4, -14}#

graph{|x+5|-9 [-19.56, 12.48, -7.99, 8.03]}

Jim G.
Apr 22, 2018

#x=-14" or "x=4#

Explanation:

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

#color(magenta)"Positive value"#

#x+5=9rArrx=9-5=4#

#color(magenta)"Negative value"#

#-(x+5)=9#

#rArr-x-5=9rArr-x=9+5=14rArrx=-14#

#color(blue)"As a check"#

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

#x=4rArr|4+5|=|9|=9#

#x=-14rArr|-14+5|=|-9|=9#

#rArrx=-14" or "x=4" are the silutions"#

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