To determine which number is the same distance away from -12 as it is from 2, we need to perform the following steps:
1. Calculate the distance between -12 and 2:
[tex]\[
\text{Distance} = |2 - (-12)|
\][/tex]
Simplifying this expression:
[tex]\[
= |2 + 12|
= |14|
= 14
\][/tex]
So, the distance between -12 and 2 is 14.
2. Check each of the given options to see which one is 14 units away from -12:
- Option (a) -14:
[tex]\[
\text{Distance} = |-14 - (-12)|
= |-14 + 12|
= |-2|
= 2
\][/tex]
The distance is 2, not 14.
- Option (b) -10:
[tex]\[
\text{Distance} = |-10 - (-12)|
= |-10 + 12|
= |2|
= 2
\][/tex]
The distance is 2, not 14.
- Option (c) -5:
[tex]\[
\text{Distance} = |-5 - (-12)|
= |-5 + 12|
= |7|
= 7
\][/tex]
The distance is 7, not 14.
- Option (d) -26:
[tex]\[
\text{Distance} = |-26 - (-12)|
= |-26 + 12|
= |-14|
= 14
\][/tex]
The distance is 14, which matches our required distance.
Thus, the number -26 is the same distance away from -12 as 2. The correct answer is:
(d) -26
