Question

If |x+2|=|x-2|, then x=________
EXPLAIN PLEASE :)

Answer 1

you really could just "guess and check"

Answer 2

i need an explanation :(

Answer 3

|...| means there is no negative so wich valu of x could do the same on both sides ?

Answer 4

Let's say X is an expression in x and b is a nonnegative number.
You solve |X| = b by solving X = b or -X = b

Answer 5

so the answer is... 4? or -2?

Answer 6

or zero?

Answer 7

i mean, in my question though.

Answer 8

my question is... How and Why? :) i just need an explanation :)

Answer 9

|x+2|=|x-2|
This is solved by turning it into these two equtions:
x + 2 = |x - 2| or -(x + 2) = |x - 2|
x + 2 = |x - 2| or -x - 2 = |x - 2|
|x - 2| = x + 2 or |x - 2| = -x - 2
Each of the two equations turns into two equations:
x - 2 = x + 2 or -(x - 2) = x + 2 or x - 2 = -x - 2 or -(x - 2) = -x - 2
no sol. or -x + 2 = x + 2 or 2x = 0 or -x + 2 = -x - 2
no sol. or -2x = 0 or x = 0 or no sol.
no sol. or x = 0 or x = 0 or no sol.
The only equations that lead to a solution give x = 0, so the only solution is x = 0.

Answer 10

You can think of it graphically also

|x+2|=|x-2|

Simply means distance of x from -2 and 2 are equal .This is only possible when x lies on y axis ie x=0 .Done :)

Answer 11

That answer is clearer. Thanks :D

Answer 12

yw :)