Identify the solution of the inequality |x + 3| - 3 / 1

Question

Identify the solution of the inequality |x + 3| - 3 >/ 1

hero · Answer

I'm assuming you mean: 

$|x + 3| - 3 \ge 1$

anonymous · Answer

Yes.

hero · Answer

Hint: Add 3 to both sides

anonymous · Answer

$$x + 3 \ge 4 $$

hero · Answer

No, you can't get rid of the absolute value sign yet:

$|x+3| \ge 4$

anonymous · Answer

How do you get rid of it then?

hero · Answer

Hint: 

$|x + a| \ge c$ becomes $ -c < x + a < c  $

anonymous · Answer

$$-4 <x+3<4$$  Now do you add it all up and set everything equal to X?

hero · Answer

Actually, let me correct my formula

hero · Answer

$|x + a| \ge c $ becomes $ -c \ge x + a \ge c$

hero · Answer

Sorry, I'm used to writing these a certain way and also I make typing errors sometimes. But that what you see above is the correct formula.

anonymous · Answer

$$-7 \le x \le1$$ Would that be the correct solution?

hero · Answer

For one, the inequality symbols are wrong. That's the reason why I corrected myself.

hero · Answer

Double check the formula again.

hero · Answer

When you do it the way I showed you, you will end up with

$-7 \ge x \ge 1$

hero · Answer

But at this point, you're probably realizing that this cannot be true.

anonymous · Answer

$$x \le -7 or x \ge 1$$

hero · Answer

May I ask how you figured that out.

hero · Answer

I was going to explain that what you posted is the correct answer.

anonymous · Answer

Isn't it because it would look like $$-7  \le  x \ge1$$

hero · Answer

No, and you still haven't explained how you figured it out. You would never write it like that.

hero · Answer

But that might give me an idea of how to write these in the future.

hero · Answer

I'm almost certain you cheated somehow.

hero · Answer

I was supposed to explain to you how to arrive at that answer.

hero · Answer

There's no way you could have figured that out on your own.

anonymous · Answer

I remember some of what I learned in school, not all of it but certain parts a little. I'm trying to figure out how I remembered it.

hero · Answer

Well, anyway, thanks to you, I can re-write my general formula.

hero · Answer

$| x + a | \ge c $ becomes $-c \le x + a \ge c$

hero · Answer

A little unconventional, but it works

hero · Answer

Actually, I just realized that the general formula may not work in every case.

hero · Answer

I'll have to test it out.