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# Absolute value and number lines

## Video transcript

we're told to plot these values on a number line and you see every one of these values have an absolute value sign so let's take a little bit of review of what absolute value even is absolute absolute value the way I think about it there's two ways to think about it the first way to think about is how far is something from zero so let me plot this negative three here so let me do a number line this isn't the number line for our actual answer or to this command plot these values on a number line this is I'm just first going to plot the numbers inside the absolute value sign and then we're going to take the absolute value and plot those just like they're asking us to do so on this number line if this is zero if we go to the negative we're going to go to the left of zero so this is negative one negative two negative three negative three sits right over there so this is negative three right there negative three right there the absolute value of negative three is essentially saying how far are you away from zero how far is negative three from zero and you say well it's one two three away from zero so you'd say that the absolute value of negative three is equal to positive three now that's really the conceptual way to imagine absolute value how far are you away from zero from zero but the easy way to calculate absolute value signs if you don't care too much about the concept is whether it's negative or positive the absolute value of it's always going to be positive absolute value of negative three is positive three absolute value of positive three is still positive three so you're always going to get the positive version of the number so to speak but conceptually you're just saying how far away are you from zero so let's do what they asked so there's that first value on this number line so all of these are absolute values so they're all going to be positive values so they're all going to be greater than zero so let me draw my number line like this I could do a straighter number line than that let's see well that's a little bit straighter and let's say if this is zero this would be negative one then you'd have one two three four five six seven I think that'll do the trick so this first quantity here I'll do it in orange the absolute value of negative three we just figure it out that is positive three so I'll plot it right over there positive three then this next value right here the absolute value of seven if we look over here one two three four five six seven seven is how far away from zero it is seven away from zero so the absolute value of seven absolute value of 7 is equal to seven so you already see the pattern there if it's negative it just becomes positive it's already positive it just equals itself so plotting this value will just place it right over there so the absolute value of 7 is 7 absolute value of negative 3 is positive 3 let me write mark out the or the zero a little bit better so you see relative to zero now we have the absolute value of 8 minus 12 the absolute value of 8 minus 12 well first of all let's figure out what 8 minus 12 is so if you take 12 away from 8 you're at negative 4 12 less than 8 is negative 4 and you can do that on the number line if you don't if this is a little bit if you don't quite remember how to do this but if you you know 1 away from if you take 8 away from 8 you're at 0 and then take another one here at negative 1 then at negative 2 negative 3 all the way to negative 4 so this is equal to the absolute value of negative 4 if we just plot absolute negative 4 we go 1 2 3 negative 4 is right over there but if we're taking its absolute value we're saying how far is negative 4 from 0 well it's 4 away from 0 1 2 3 4 so this is equal to positive 4 so we'll plot it right here this number line is the answer to this command up here so the absolute value of 8 minus 12 negative 4 is positive 4 then we have the absolute value of 0 of 0 so how far is 0 from 0 well it's 0 away from 0 the absolute value of 0 is 0 so you can just plot it right over there and we have one left let me pick a suitable color here the absolute value of 7 minus 2 the absolute value of 7 minus 2 well 7 minus 2 is 5 so this is the same thing as the absolute value of 5 how far is 5 away from 0 well it's just 5 away it's almost you know too easy that's what makes it confusing if I were to plot 5 it's 1 2 3 4 5 it is 1 2 3 4 5 spaces from 0 so the absolute value of 5 is 5 if you plot it just like that so conceptually it's how far you are away from 0 but if you think about it in kind of just very simple terms if it's a negative number it becomes a positive version of it if it's a positive number already it just equals itself when you take the absolute value