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

Express the distance between the numbers 2 and 17 using absolute value. Then find the distance by evaluating the absolute value expression ?
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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 $|x-y|$.
Put 2 for x and 17 for $y\in |x-y|$.
$|x-y|=|2-17|$
$=|-15|$
The absolute value function is defined by $|x|=\left\{\begin{array}{cc}x& x\ge 0\\ -x& x<0\end{array}$.
Since -15 < 0, it can be concluded that $|-15|=-\left(-15\right)$.
$|-15|=15$
The distance between the points 2 and 17 is expressed as $|2-17|$ and the value of the expression is 15 units.