Question

move numbers to the lines to create two absolute value expressions that represent the distance between the two points on the number line.
expression a: |-10 - (___)|
expression b: |-10 + (___)|
numbers: -6, -4, 4, 6

Explanation:

Step1: Recall distance absolute value formula

The distance between two numbers $a$ and $b$ is $|a-b|$ or $|b-a|$, which can also be written as $|a+(-b)|$.

Step2: Fill Expression A

For $|-10 - (\underline{\quad})|$, use the second point $-4$.
$|-10 - (-4)|$

Step3: Simplify to verify match

$|-10 - (-4)| = |-10 + 4| = |-6| = 6$, which is the distance.

Step4: Fill Expression B

For $|-10 + (\underline{\quad})|$, rewrite $|-10 - (-4)|$ as $|-10 + 4|$, so the blank is $4$.
$|-10 + 4|$

Step5: Verify Expression B

$|-10 + 4| = |-6| = 6$, which is the correct distance.

Answer:

Expression A: $|-10 - (-4)|$
Expression B: $|-10 + 4|$