Which of these statements about absolute value is FALSE?

Class 6IntegersIntegers

A|−8| = 8
B|0| = 0
C|−8| = −8
D|8| = 8

Step-by-Step Solution

Absolute value is a distance from zero, and a distance is never negative. So |−8| = 8, not −8, which makes the third statement the false one. The trap is thinking the bars simply keep whatever sign was already there.

Answer: C) |−8| = −8

Key idea: Adding integers — different signs

When two integers have **different signs**, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value. So 7 + (−3) = 4 (|7| > |−3|, so the answer is positive 4), and (−7) + 3 = −4 (|−7| > |3|, so the answer is negative 4). On the number line: a positive number moves right, a negative number moves left — they partially cancel.

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