Question

what is one way to find the distance? find $-15 - 7$. then take the absolute value. what is another way to find the distance? find $7 - ?$. then take the absolute value. options for ?: $(-15)$, $15$. (number line image: points at -15, 0, 7)

Explanation:

Step1: Recall distance formula on number line

The distance between two numbers \(a\) and \(b\) on the number line is \(|a - b|\) or \(|b - a|\) (since absolute value makes them equal).

Step2: Identify the two numbers

The two numbers on the number line are \(-15\) and \(7\). So for the expression \(7 -?\), the "?" should be \(-15\) because the distance is \(|7 - (-15)|\) (which is the same as \(|7 + 15|=|22| = 22\), and also \(|-15 - 7|=|-22| = 22\)).

Answer:

\((-15)\)