Question

I am trying to solve an equation with 2 absolute values and am running into something where I have the answer but I don't know why.

|2n+3| = |3+2n| is the problem

To solve I did:
2n+3 = 3+2n or 2n+3 = -3-2n
My answers were
0=0 or -3/2

Answer in the book was
All Real Numbers

Can someone tell me why? I want to understand the answer, not just copy it...
TIA

Answer 1

2n+3 is exactly same as 3+2n
so this will be satisfied by every real number.

Answer 2

I saw that they were the same on both sides (just not in the same order), I just didnt see in the book where it explained that because they were the same, that meant the answer could be every real number. I am very careful to make sure I understand the "why" of a problem and this one was new to me.

Answer 3

Oh, and thanks!!

Answer 4

ok, mathematically u get 0=0, right ?
so this implies |2n+3| = |3+2n| is an identity.
and an identity is one which is satisfied by all real numbers

Answer 5

I do see now. (it seems so much simpler once someone else said it). I was over thinking it - like the answer was too simple so where is the trick ya know?

Answer 6

glad i could help.

Answer 7

every value of \(n\) will satisfy the equation

Answer 8

You did :) Thanks again