Express the distance between the numbers 2 and 17 using absolute value. Then find the distance by evaluating the absolute value expression ?

Step 1
The two numbers 2 and 17.
Step 2
The distance between two numbers is represented by their difference. As the distance is always a positive quantity, the absolute value function is used over the distance to prevent a negative distance.
The distance between points x and y is given by ${\displaystyle \left|x-y\right|}$.
Put 2 for x and 17 for ${\displaystyle y\in \left|x-y\right|}$.
${\displaystyle \left|x-y\right|=\left|2-17\right|}$
${\displaystyle =\left|-15\right|}$
The absolute value function is defined by ${\displaystyle \left|x\right|=\{\begin{array}{cc}x& x\ge 0\\ -x& x<0\end{array}}$.
Since -15 < 0, it can be concluded that ${\displaystyle \left|-15\right|=-(-15)}$.
${\displaystyle \left|-15\right|=15}$
The distance between the points 2 and 17 is expressed as ${\displaystyle \left|2-17\right|}$ and the value of the expression is 15 units.