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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