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## Main Question or Discussion Point

Assumption: |x| is unconditionally equal to ±x.

This makes sense because if you take a look at a graph of y=|x|, and plot any horizontal line y=C where C is some constant, you will always have two solutions: one is positive and one is negative.

But if we substitute any number into x, then we realize that this actually contradicts:

|x| = ±x

Let x = 2

|2| = ±2

2 = ±2

2 = 2 OR 2 = -2

Am I missing something or is the only reason why they aren't unconditionally equal?

This makes sense because if you take a look at a graph of y=|x|, and plot any horizontal line y=C where C is some constant, you will always have two solutions: one is positive and one is negative.

But if we substitute any number into x, then we realize that this actually contradicts:

|x| = ±x

Let x = 2

|2| = ±2

2 = ±2

2 = 2 OR 2 = -2

Am I missing something or is the only reason why they aren't unconditionally equal?

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