10
algebra

Solve: x5+x+510|x - 5| + |x + 5| \leq 10

A

5x5-5 \leq x \leq 5

B

x=0x = 0

C

No solution

D

All real numbers

Correct Answer: A

Choice A is the correct answer. Geometric interpretation.

  1. Concept: Sum of distances from 5 and -5 is 10\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> 10.
  4. Result: The segment [5,5][-5, 5].

?�� Strategic Tip:xa+xb=ab|x-a| + |x-b| = |a-b| is true for all xx between aa and bb.

Choice B is incorrect because it is only one point. Choice C is incorrect.Choice D is incorrect.