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

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Answer 1 · 2018-06-22T19:31:03

$x \in ϕ$ $x in phi$

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

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

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