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.

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)   (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)   (Show Source): 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
Answer by bucky(2189)   (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:
.

.
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.
RELATED QUESTIONS
Solve Equation Problem: 16^-x+2=8 -x+2=log16(8) Have I started this... (answered by jsmallt9)
-2^3-1/-2^-2(x+2)-3x=-2^0(-2x^0-4) This is how I worked it out at one point but I cant (answered by stanbon)
" what is the slope of {{{ 2x+3 }}}" "i have never understood this so please explain... (answered by stanbon)
I'm so lost on this one. I do remember the order of operations, however this is a very... (answered by rapaljer)
I am trying to solve y=x2-6x. so far column x is 0 1 2 3 4 column y is 0 -5 -8 a=1... (answered by KnightOwlTutor)
i need help on this problem it is 8 and 1 third divided by 3 and 3 forths i tried so many (answered by josmiceli)
I seem to be having issues with the equations with fractions in them. I'm getting... (answered by CubeyThePenguin,MathTherapy)
Could you please help me with this? I have a huge final this week. I believe the answer... (answered by jim_thompson5910,stanbon)
The Binomial Theorem...When (2a + b)^8 is expanded, what is the coefficient of the term... (answered by scott8148)