Question

the number line shows the locations of -3, 0, and 3. choose all of the expressions which describe a distance of 3 units on the number line. a. |-10 - (-3)| b. |0 - 3| c. |0 - (-3)| d. |-13 - 0| e. |3 - 0| f. |-3 - 0|

Explanation:

Step1: Evaluate Option A

$-\vert0 - (-3)\vert = -\vert3\vert = -3$
Distance is non-negative, so this is not a distance of 3.

Step2: Evaluate Option B

$\vert0 - 3\vert = \vert-3\vert = 3$
This equals 3, a valid distance of 3 units.

Step3: Evaluate Option C

$\vert0 - (-3)\vert = \vert3\vert = 3$
This equals 3, a valid distance of 3 units.

Step4: Evaluate Option D

$-\vert3 - 0\vert = -\vert3\vert = -3$
Distance is non-negative, so this is not a distance of 3.

Step5: Evaluate Option E

$\vert3 - 0\vert = \vert3\vert = 3$
This equals 3, a valid distance of 3 units.

Step6: Evaluate Option F

$\vert-3 - 0\vert = \vert-3\vert = 3$
This equals 3, a valid distance of 3 units.

Answer:

B. $\vert0 - 3\vert$, C. $\vert0 - (-3)\vert$, E. $\vert3 - 0\vert$, F. $\vert-3 - 0\vert$