Question

question 11 of 25
which number line and expression show how to find the distance from 2 to -5?
a.
( |2 - (-5)| )

b.
( |-2 - (-5)| )

c.
( |2 - 5| )

d.
( |-2 - 5| )

Explanation:

Step1: Recall distance formula

The distance between two numbers $a$ and $b$ on a number line is $|a - b|$. For $a=2$, $b=-5$, this is $|2 - (-5)|$.

Step2: Verify number line count

Count units from 2 to -5: $2$ to $1$ (1), $1$ to $0$ (1), $0$ to $-1$ (1), $-1$ to $-2$ (1), $-2$ to $-3$ (1), $-3$ to $-4$ (1), $-4$ to $-5$ (1). Total: $7$ units.

Step3: Evaluate the expression

$|2 - (-5)| = |2 + 5| = |7| = 7$, which matches the number line in option A.

Step4: Eliminate other options

• Option B: Expression $|-2-(-5)|=|3|=3$, incorrect distance.
• Option C: Expression $|2-5|=|-3|=3$, counts distance to 5, not -5.
• Option D: Expression $|-2-5|=|-7|=7$, but number line does not match 2 to -5.

Answer:

A. $|2-(-5)|$ with the number line showing the distance from 2 to -5