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.

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