Question

# 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

Piecewise-Defined Functions
Which of the following correctly uses absolute value to show the distance between -80 and 15?
A.
$$\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}=-{95}$$ units
B.
$$\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}={65}$$ units
C.
$$\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}={95}$$ units
D.
$$\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}=-{65}$$ units

2021-02-13
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 $$\displaystyle{\left|{{a}−{b}}\right|}{\quad\text{or}\quad}{\left|{{b}−{a}}\right|}$$
$$\displaystyle\Rightarrow$$ The distance between - 80 and 15 is $$\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}$$, but absolute value changes a negative number into its positive additive inverse.
$$\displaystyle\Rightarrow{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}={95}$$ units.
Hence, option (c) is correct.