Absolute Value of $|-3 -2|$

Question

$|-3 -2|$ is the distance between the points $-3$ and $-2$. If we solve it further then,

in one way I get $|-5| = 5$. But $5$ is the distance between $0$ and $-5$ in this case. In other way,

$2 -(-3) = 5$. By adopting this way, we also get the same answer.

what if, $-2 -(-3) = 1$. $1$ this seems to be the distance between -2 and -3. So which way is the correct one?

Answer 1

Distance between two points a,b on real line is $|a-b|$. and not $|a+b|$.

Now see $|-3-2|=|(-3)-(2)|$ ie distance between $-3$ and $2$ .

Now it's done.

Answer 2

As you said, if you denote $d_1$ the distance between $-2$ and $-3$, then $d_1=|-2-(-3)|$

In the same way, if you denote $d_2$ the distance between $-3$ and $-2$., then $d_2=|-3-(-2)|$

Then, $d_1=|-2-(-3)|=|-2+3|=|-(-2+3)|=|2-3|=|-3+2|=|-3-(-2)|=d_2$

Note: $|-2+3|=|-(-2+3)|$ because for any value $a$, you have $|a|=|-a|$

So you see you actually do have two ways of determining the distance between two points $a$ and $b$ either by saying it's $|a-b|$ or $|b-a|$. There is no "correct way", both are. Just be careful with the signs. If you're not at ease with this yet you should always put your values in parenthesis first like such:

$$|(-3)-(-2)|$$