Set 6: Linear Inequalities (Advanced)

Choice A is correct. Choice A is the correct answer. Geometric interpretation. 1. Concept: Sum of distances from 5 and -5 is $\leq 10$. 2. Distance between foci: Distance between 5 and -5 is 10. 3. Logic: The sum of distances to endpoints of a segment is equal to the length of the segment ONLY for points ON the segment. For points outside, the sum is $> 10$. 4. Result: The segment $[-5, 5]$. Strategic Tip: $|x-a| + |x-b| = |a-b|$ is true for all $x$ between $a$ and $b$. Choice B is incorrect because it is only one point. Choice C is incorrect. Choice D is incorrect.