Question

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

Answer 1

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]}

Answer 2

`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"`