Question

Can anyone prove the following?
abs(x)= abs(-x)

Answer 1

Absolute value means distance from zero.

Answer 2

x and its opposite, -x are both the same distance from zero, regardless of what x is.

Answer 3

abs(-x) = abs(-1 * x) = abs(-1) * abs(x) = 1 * abs(x) = abs(x)

Answer 4

@Coolsector that looks a bit circular. Can you prove that abs(-1)=abs(1). If you sub in x=-1, then you are back where you started.

Answer 5

proofs are just that though- circular

Answer 6

Not always. Circular reasoning isn't technically logically invalid, but it is ... less appealing.
Majority of proofs are deductive or inductive without requiring tautology.