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If the inequality |a| < |b| is true, which of the following must be true?

A) a = b
B) a ≠ b
C) a > b
D) a < b

User Srajeshnkl
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Final answer:

The inequality |a| < |b| indicates that the magnitude of a is less than the magnitude of b, which means option B) a ≠ b must be true since a and b cannot be equal in magnitude.

Step-by-step explanation:

If the inequality |a| < |b| is true, then this means the absolute value of a is less than the absolute value of b. It does not inform us about the actual values of a and b, only about their magnitudes. Therefore, this inequality does not imply that a is greater than, less than, or equal to b in actual value, but only that the magnitude of a is less than the magnitude of b. So options A) a = b, C) a > b, and D) a < b could be true in specific cases but are not guaranteed by the inequality given. The only conclusion we can draw with certainty is that a is not equal to b in magnitude, which reflects option B) a ≠ b.

User Omri Ben Lulu
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