Question

The distance between a and b on the real line is $d\left(a,b\right)=$_______.

So, the distance between $-5$and 2 is _______.

Short answer

The distance between a and b on the real line is $d\left(a,b\right)=\underset{¯}{\left|b-a\right|}$. So, the distance between$-5$ and 2 is7.

Step-by-step solution

Step 1. State the concept.

The distance between two real numbers a and b on the real line is given as $d\left(a,b\right)=\left|b-a\right|$.

Step 2. List the given data.

The given incomplete statements are as follows:

The distance between a and b on the real line is $d\left(a,b\right)=$________. So, the distance between $-5$and 2 is _____.

Step 3. Complete the statement.

Put $a=-5$and $b=2$in $d\left(a,b\right)=\left|b-a\right|$to get,

role="math" localid="1643022186090" $\begin{array}{c}d\left(-5,2\right)=\left|2-\left(-5\right)\right|\\ =\left|2+5\right|\\ =\left|7\right|\\ =7\end{array}$

So, $d\left(-5,2\right)=7$.

Applying the definition of distance between two real numbers and using $d\left(-5,2\right)=7$, the complete statements are:

The distance between a and b on the real line is $d\left(a,b\right)=\underset{¯}{\left|b-a\right|}$. So, the distance between $-5$and 2 is 7.