Question

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

Answer 1

What's stopping you from solving it?

Answer 2

One sec not sure if I did it correctly.

Answer 3

When you multiply x + 3 by 2 do you make the 2 a negative.

Answer 4

No, don't do that. This one is WAY easier. Just add 2 to both sides and then let's talk. Show me what you get.

Answer 5

k

Answer 6

x+5 = -5

Answer 7

No. Why did the absolute values disappear?

|x + 3| – 2 + 2 = –5 + 2

|x + 3| = -3

You need to believe this. We have done nothing with the absolute values.

Answer 8

Yikes my bad. Alright I should be able to do this.

Answer 9

Whoa!! Let's talk. Do yousee how we got to this? |x + 3| = -3?

Answer 10

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

Answer 11

So x = -6

Answer 12

or 0

Answer 13

You are not talking, you're just guessing. Let's just stop here and talk.

|x+3| = -3

Answer this question. When you find the absolute value of something (other than zero), what is the sign after you are done?

|3| = 3
|-2| = 2
|8| = 8
|-12| = 12

Answer 14

Well if it's a positive it would turn to a negative, no?

Answer 15

No, look at |-2|. It turns that into +2

Negative numbers are made positive.
|-2| = 2
|-8| = 8
Positive numbers are already positive so nothing happens.
|3| = 3
|9| = 9

The absolute value cannot EVER be negative. Do you believe this?

Answer 16

Yes.

Answer 17

Perfect. Now, let's look at what we have.

1) The absolute value cannot EVER be negative.
2) |x+3| = -3

There is a problem with these two statements. Do you see it?

Answer 18

All I should focus on is fixing the negatives to positive in this step.

Answer 19

k

Answer 20

when I turn the negative 3 positive are the other numbers effected?

Answer 21

There is no absolute value associate with -3. Don't do that. Read it as it is. Don't make things up.

Look at those two statements again. Something is seriously wrong with those two statements.

Maybe a short story will help...

Son: Dad, I wrecked the car.
Dad: What? Is everyone okay?
S: Well, there were no injuries, but we couldn't drive the car home.
D: What happened?
S: I was goofing off to impress my girlfriend and I just lost control and ran into a tree.
D: Well, you know what this means, don't you?
S: No, but I figured it would be bad...
D: That's right. I have to revoke your driving privileges. You will NEVER drive another car as long as you live.
S: But...but...
D: Here's the keys, Son. Take the other car and go down to the store to get some milk and eggs.

That's a geat story, isn't it? Dad may have been a little harsh.

In any case, look at Dad's last two statements. Do you see anything wrong with them, taken together?

Answer 22

Ones negative then the other is positive.

Answer 23

?? One says "never" and the other simply allows it. The term for this is "inconsistent". They cannot possibly exist at the same time and be consistent.

Now back to our problem. Look at these two statements:

1) The absolute value cannot EVER be negative.
2) |x+3| = -3

Are they consistent? Can they both be correct at the same time?

Answer 24

no

Answer 25

Well first you add 2 to both sides to isolate the absolute value

Answer 26

Done that already.

Answer 27

Then you make two sides, one negative, one positive side