# Which of the following correctly uses absolute value to show the distance between -80 and 15? A. abs(-80 - 15) = abs(-95) = -95 units B. abs(-80 + 15) = abs(-65) = 65 units C. abs(-80 - 15) = abs(-95) = 95 units D. abs(-80 + 15) = abs(-65) = -65 units

Which of the following correctly uses absolute value to show the distance between -80 and 15?
A.
$|-80-15|=|-95|=-95$ units
B.
$|-80+15|=|-65|=65$ units
C.
$|-80-15|=|-95|=95$ units
D.
$|-80+15|=|-65|=-65$ units
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Step 1
Our aim is to calculate the distance between −80 and 15 using absolute value.
Step 2
The distance between any two points a and b on th enumber line is $|a-b|\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}|b-a|$
$⇒$ The distance between - 80 and 15 is $|-80-15|=|-95|$, but absolute value changes a negative number into its positive additive inverse.
$⇒|-80-15|=|-95|=95$ units.
Hence, option (c) is correct.