Choice A is the correct answer. Analyze the definition of absolute value.

1. Equation: $|x| = -x$
2. Definition: $|x| = -x$ is true if and only if $x$ is non-positive ($x \leq 0$).
   • If $x = -5$: $|-5| = -(-5) = 5$ (True).
   • If $x = 0$: $|0| = -0 = 0$ (True).
   • If $x = 5$: $|5| = -5$ (False).
3. Result: $x \leq 0$

?�� Strategic Tip:$|x| = x$ for $x \geq 0$. $|x| = -x$ for $x \leq 0$.

Choice B is incorrect because it misses negative numbers. Choice C is incorrect because it misses 0. Choice D is incorrect because solutions exist.