Question

What is the solution set of |x + 3| – 2 = –5?

Answer 1

You see that
|x+3| = -3

Do you agree so far?

Answer 2

I have no idea what to do, honestly.

Answer 3

Ok. So, I added 2 to each side

|x+3| - 2 + 2 = -5 + 2

Hence

|x+3| + 0 = -3
|x+3| = -3

Yes?

Answer 4

Oh. okay. I see now...

Answer 5

either x+3 or -x-3 would be used to replace the absolute value sign so..

x + 3 - 2 = 5 or -x - 3 - 2 = 5

solve

Answer 6

Good. Now we have a problem.

Answer 7

@gspade: totally wrong, sorry.

Is there ANY number y such that |y| = -3 ?

Answer 8

Because |3| = 3 and |-3| = 3.

So is there any number y such that |y| = -3 ?

Answer 9

agree with JamesJ

Answer 10

So to recap. So far we shown the original problem is equivalent to the problem of find x such

|x+3| = -3

Now the question I am raising is this: can that equation even have any solutions in theory?

Answer 11

That is, are there ANY numbers y that have the property that
| y | = -3 ?

Answer 12

Ok. You've buggered off. But think about what I'm asking. Good luck.