SOLUTION: Have I understood this correctly? I get confused very easy at times! I believe this is true. |-8| + |3| = |-8 + 3| Thanks so much for your time.

Algebra ->  Number-Line -> SOLUTION: Have I understood this correctly? I get confused very easy at times! I believe this is true. |-8| + |3| = |-8 + 3| Thanks so much for your time.      Log On


   

Question 112393: Have I understood this correctly? I get confused very easy at times! I believe this is true. |-8| + |3| = |-8 + 3| Thanks so much for your time.
Found 3 solutions by Earlsdon, Fombitz, bucky:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The absolute value of a number can be defined as its distance from zero on the number line.
So:
|-8| = 8 and
|3| = 3, therefore:
|-8| + |3| = 8 + 3 = 11

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, that's not correct.
Remember the definition of the absolute value function,
abs%28x%29=x if x%3E=0
abs%28x%29=-x if x%3C0
Let's look at your values separately.
abs%28-8%29=-%28-8%29=8
abs%283%29=3
abs%28-8%2B3%29=abs%28-5%29=-%28-5%29=5
If we use you equality, then
abs%28-8%29%2Babs%283%29=abs%28-8%2B3%29
8%2B3=5
11=5
The absolute value function has the following property, called subadditivity,
abs%28x%2By%29%3C=abs%28x%29%2Babs%28y%29
and in your case leads to
abs%28-8%2B3%29%3C=abs%28-8%29%2Babs%283%29
5%3C=11
which is a true statement

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let's try to straighten out the confusion by using a rule. Whatever the sign of a quantity
inside the absolute value signs, when you remove the absolute value signs that quantity
will be positive.
.
So lets start with:
.
abs%28-8%29+%2B+abs%28%2B3%29
.
You can remove the absolute value signs around the -8, but when you do that you change it
to a +8. And you can remove the absolute value signs around the +3, and it remains a +3.
So the problem becomes:
.
abs%28-8%29+%2B+abs%28%2B3%29+=+%2B8+%2B+3+=+%2B11
.
Now let's look at what you believed to be equivalent:
.
abs%28-8+%2B+3%29
.
First you have to algebraically combine the terms inside the absolute value signs:
.
-8+%2B+3+=+-5
.
This converts your answer to:
.
abs%28-5%29
.
And applying the rule ... remove the absolute value signs, and make sure the quantity
they contained now has a plus sign. This means:
.
abs%28-8+%2B+3%29=abs%28-5%29+=+%2B5
.
Notice that the two answers ... +11 and +5 ... are not the same. The correct answer to
this problem is +11.
.
Hope this helps you to understand absolute values a little better.