College Algebra, What is this?

[CLEP101]

How is this one done?

If 5 + m = n, what is the value of 2|m – n|?

a. −10

b. −5

c. 5

d. 10

e. It cannot be determined from the given information.

[gcalvin]

5 + m = n

2|m - n| =
2|m - (5 + m)| =
2|m - 5 - m| =
2| -5 | =
2 * 5 = 10

Answer (d) is correct.

-Gary-

[CLEP101]

5 + m = n

2|m - n| =
2|m - (5 + m)| =
2|m - 5 - m| =
2| -5 | =
2 * 5 = 10

Answer (d) is correct.

-Gary-

So in this case, the m cancels out because you combine the like terms which one is negative and one a positive. I'm assuming that the two lines outside the -5 are asking for the absolute value of the -5 which would be positive 5 and multiplied by 2?
I just want to make sure I got it.
Thanks Gary

[gcalvin]

That's right. I don't much like "cancels out" as it seems vague and sloppy and ultimately not helpful. It's really just that m - m = 0. A lot of people use "cancels out" for something like m/m = 1 also, but I think it's better to think clearly and explicitly about both those cases. You're absolutely right about absolute value: | -5 | = 5.

-Gary-

[nj593]

I didnt look at it in depth but would imagine 10 because it says 5 is m which is n times that and you get 10 atleast in my warped math head:p

How is this one done?

If 5 + m = n, what is the value of 2|m – n|?

a. −10

b. −5

c. 5

d. 10

e. It cannot be determined from the given information.