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Set 9: Linear Inequalities (Advanced)

Explanation

Answer: B

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

✓ Correct
C.

5<x<5-5 < x < 5

D.

x5x \geq 5

Detailed Explanation

Choice B is correct. 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 because 5\geq 5 includes 5 itself (which is exactly 5 units away, not more than), and misses negative numbers.

Key Steps:

The correct answer is x<5x < -5 or x>5x > 5

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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