# How do you solve |x+45| = -6?

Jun 22, 2018

$x \in \phi$

#### Explanation:

we have $| x + 45 | = - 6$
now we have two cases

• Case 1((x+45)>=0;x>=-45........(a)
$\left(x + 45\right) = - 6$
x=-6-45; x=-51.........(b)
from (a) and (b) we get
$x \in \phi$
• Case 2((x+45)<0;x<-45......(d)
$- \left(x + 45\right) = - 6$........(a negative sign is there because for any value of x<-45,(|A|), A will be negative)
now we get $x = - 39$..............(e)
Again from (d)and (e)
$x \in \phi$
hence there is no real solution for x
i.e. $x \in \phi$