5
algebra

Which inequality represents all numbers that are more than 5 units away from 0?

A

x>5x > 5

B

x<5x < -5 or x>5x > 5

C

5<x<5-5 < x < 5

D

x5x \geq 5

Correct Answer: B

Choice B is the correct answer. Distance from zero on a number line involves both positive and negative directions.

  1. Understanding: "More than 5 units from 0" means farther than 5 in EITHER direction
  2. Positive side: Numbers >5> 5 (like 6, 7, 100)
  3. Negative side: Numbers <5< -5 (like -6, -7, -100)
  4. Combine with OR: x<5x < -5 or x>5x > 5

?�� Strategic Tip: Distance problems often use "or" to combine two separate regions on the number line.

Choice A is incorrect because it only captures positive numbers beyond 5, missing the negative side. Choice C is incorrect because this represents numbers WITHIN 5 units of 0, the opposite of what we want. Choice D is incorrect because5\geq 5 includes 5 itself (which is exactly 5 units away, not more than), and misses negative numbers.