Question

Determine whether x is positive or negative in the following equation:
x-|x|=0

Answer 1

test for a negative:
let x = -5
Left side = -5 - |-5
= -5-5 = -10
≠ RS

test for x = 0,
LS = RS

test for postive x
let x = 5
LS = 5 - |5| = 0 = RS

so x ≥ 0

Answer 2

Recall the definition of |x|:
|x| = x if x >= 0
|x| = -x if x < 0

Now, your equation is

x-|x|=0
x = |x|
so, x >= 0