Question

Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
4 and 15

Answer 1

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