Set 9: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Check for extraneous solutions. 1. Case 1: $x - 2 = 2 x - 7 \rightarrow -x = -5 \rightarrow x = 5$ - Check: $|5-2| = 2(5)-7 \rightarrow 3 = 3$ (Valid) 2. Case 2: $x - 2 = -(2 x - 7) \rightarrow x - 2 = -2 x + 7 \rightarrow 3 x = 9 \rightarrow x = 3$ - 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.