how to find absolute value
Answers
Solving by Substituting Variables
So we know that absolute values make things positive, but how does that effect how we evaluate absolute values at specific values? Let's take a look at an example:
Evaluate m|5-2n|+7, when m equals -2 and n equals 10. This problem is actually no more different than any other problem that asks us to substitute in values as long as we don't fall into the biggest absolute value pitfall; the absolute value bars DO NOT change subtraction symbols into addition ones. Yes, they do make things positive, but only after you've completed whatever operations are going on on the inside.
So if we first substitute in -2 for m and 10 for n, we treat the absolute value bars like parentheses and we begin on the inside of them. Multiplication comes before subtraction, so I do 2*10 and I get 20. Then I do 5-20 and end up with -15, and only at that point, after I've finished all the different things on the inside of the absolute value, do we actually take the absolute value, making -15 positive 15. Again, because absolute value bars are kind of like parentheses, when you have a number in front it means multiplication, and -2*15 is -30. Last but not least, -30+7 is -23.
