# Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 4 and 15 Question
Piecewise-Defined Functions Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
4 and 15 2020-10-27
Step 1
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
4 and 15
Step 2
We know that,the distance between p and q is given by $$\displaystyle{\left|{{p}-{q}}\right|}{\quad\text{or}\quad}{\left|{{q}-{p}}\right|}$$.
So, the distance between 4 and 15 is $$\displaystyle{\left|{{4}-{15}}\right|}{\quad\text{or}\quad}{\left|{{15}-{4}}\right|}$$
Now, for $$\displaystyle{\left|{{4}-{15}}\right|}$$
$$\displaystyle\Rightarrow{\left|{{4}-{15}}\right|}={\left|{-{11}}\right|}$$
$$\displaystyle\Rightarrow{\left|{{4}-{15}}\right|}={11}$$
Now, for $$\displaystyle{\left|{{15}-{4}}\right|}$$
$$\displaystyle\Rightarrow{\left|{{15}-{4}}\right|}={\left|{-{11}}\right|}$$
$$\displaystyle\Rightarrow{\left|{{15}-{4}}\right|}={11}$$
On solving both $$\displaystyle{\left|{{4}−{15}}\right|}{\quad\text{or}\quad}{\left|{{15}−{4}}\right|}$$ we get 11
Therefore,the distance between 4 and 15 is 11

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A.
$$\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}=-{95}$$ units
B.
$$\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}={65}$$ units
C.
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D.
$$\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}=-{65}$$ units 