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### Course: 7th grade>Unit 4

Lesson 1: Absolute value

# Interpreting absolute value as distance

In this video, we work through a bunch of examples that stretch our thinking on absolute value.

## Want to join the conversation?

• What if the absolute value was 0
• The absolute value is the distance from zero. If the absolute value of a number is zero, that number itself is also zero.
• help! I don't get anything of this absolute value part . its very frustrating :(
• I'm not sure what don't you understand, but absolute value is simply THE DISTANCE FROM THE NUMBER TO 0. For example, if you imagine two numbers on a number line: -4 to 0. That would be four blocks away right? Which means, the absolute value of -4 is 4. If you have any other questions you can reply to this. I will be checking them :)
• This is 11 minutes long... WHY!!
• At the point, Sal quickly scribbles out the third option.
Although, I tried out this proposition with the values:
x = 5
and y = 9
Which gives the equation:
|11 - 9| = |-5 - (-3)|
and both sides of the equation equal 2.
So the third option, does in fact work.
• Help! Is the equation |a-b|=|a|-|b| true all the time or just only for this special case?

at , sal agreed that |a-b| is the same thing as |a|-|b|
also in a previous video sal said |a-b| = |b-a|

so, it seems like we can say |b-a| = |b|-|a|.
if this is logical then why the following equation is not true:
let's imagine a=-9 and b=-2
|a|-|b|=|b|-|a|
⇒ |-9|-|-2| = |-2|-|-9|
⇒ 9-2 = 2-9
⇒ 7 ≠ -7

thanks in advance 🙂
• Good question. |a-b|=|b-a| is always true because the distance between the two are the same no matter which side you start from. However, |b-a|=|b|-|a| when a and b are the same signs. The second rule would be |b-a|=|b|+|a| if they are opposite signs. Your assumption that is special case is correct, but there are only two choices. I am not sure |a|-|b| ever equals |b|-|a| unless |b|=|a|.
• What is the distance between a and b?
• A and B are variables, so it depends what A and B are. if A=1 and B=(-2) then the answer is 3.
• At to he says the absolute value of a-b is the same thing as b-a. I don't understand how that is possible. It's making me nuts crazy and confused.
• what if the absolute value is x