Choice A is the correct answer. Check for extraneous solutions.

1. Case 1: $x - 2 = 2x - 7 \rightarrow -x = -5 \rightarrow x = 5$
   • Check: $|5-2| = 2(5)-7 \rightarrow 3 = 3$ (Valid)
2. Case 2: $x - 2 = -(2x - 7) \rightarrow x - 2 = -2x + 7 \rightarrow 3x = 9 \rightarrow x = 3$
   • Check: $|3-2| = 2(3)-7 \rightarrow 1 = -1$ (Invalid!)
3. Result: Only $x = 5$

?�� Strategic Tip: Always plug answers back into absolute value equations. $|A| = B$ requires $B \geq 0$.

Choice B is incorrect because it is an extraneous solution. Choice C is incorrect because it includes the extraneous solution. Choice D is incorrect because$x=5$ is valid.