How do you solve #|x + 3| = (x-2)#?

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Answer 1 · 2017-04-14T10:27:03

No solution

Since absolute values are always nonnegative,

#|x+3|=x-2 geq0 Rightarrow x geq 2#,

which means that #x+3# is nonnegative.

So, the equation becomes (by simply removing the absolute value sign)

#Rightarrow x+3=x-2#

By subtracting #x# from both sides,

#Rightarrow 3=-2#,

which is false.

Hence, there is no solution.

I hope that this was clear.

Answer 2 · 2017-04-14T13:11:50

No real solution.

We have

#abs(x+3)=x+3-5# or assuming #x ne -3#

#1=(x+3)/abs(x+3)-5/abs(x+3)# so there are two possibilities

#{(1=1-5/abs(x+3)),(1=-1-5/abs(x+3)):}#

and in both cases there is not a real solution for the equations.