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.

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

You can put this solution on YOUR website!
No, that's not correct.
Remember the definition of the absolute value function,
if
if
Let's look at your values separately.



If we use you equality, then



The absolute value function has the following property, called subadditivity,

and in your case leads to


which is a true statement

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:
.

.
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:
.

.
Now let's look at what you believed to be equivalent:
.

.
First you have to algebraically combine the terms inside the absolute value signs:
.

.
This converts your answer to:
.

.
And applying the rule ... remove the absolute value signs, and make sure the quantity
they contained now has a plus sign. This means:
.

.
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.