Comparing absolute values

let's do some examples comparing absolute values so let's say we were to ask ourselves how negative 9 the absolute value of negative 9 I should say how that compares how that compares to the absolute value of let me think of a good number let's say the absolute value of negative 7 so let's think about this a little bit and let's think about what negative 9 looks like or where it is on the number line where negative 7 is on the number line let's see whether their absolute values mean and then we should probably be able to do this comparison so there's a couple of ways to think about it one is you can draw them on the number line so if this is 0 if this is negative 7 and then this is negative 9 right over here now when you take the absolute value of a number you're really saying how far is that number from 0 whether it's to the left or to the right of 0 so for example negative 9 is 9 to the left of 0 so the absolute value of negative 9 is exactly 9 this evaluates to 9 negative 7 is exactly 7 to the left of 0 is exactly 7 to the left of 0 so the absolute value of negative 7 is positive 7 and so if you were to compare 9 & 7 this is a little bit more straightforward 9 is clearly is clearly greater than 7 and if you ever get confused with the greater than or less than symbols just remember that the symbol is larger on the left hand side so that's the greater than side if I were to write this and this is actually also a true statement if you took up these without the absolute value signs it is also true that negative 9 is less than is less than negative 7 notice the smaller side is on the smaller number and so that's the interesting thing negative 9 is less than negative 7 but their absolute values since negative 9 is further to the left of 0 it is the absolute value of negative 9 which is 9 is greater than the absolute value of negative 7 another way to think about it is if you take the absolute value of a number it's really just going to be the positive version of that number so if you took the absolute value of nine take the absolute value of nine that equals nine or the absolute value of negative nine that is also equal to nine when we think of it visually that's because both of these numbers are exactly nine away from zero this is nine to the right of zero and this is nine to the left of zero let's do a few more of these so let's say that we wanted to compare we wanted to compare the absolute value of two to the absolute value of three well the absolute value of a positive number is just going to be that same value two is two to the right of zero so this is just going to evaluate to two and then the absolute value of three that's just going to evaluate to three it's actually pretty straightforward so two is clearly the smaller number here and so we clearly get two is less than three or the absolute value of two is less than three so we have a less than right over here let's say you wanted to compare you wanted to compare I'm trying to find a suitable color the absolute value of negative eight to the absolute value of eight well one way to think about it is that they are both eight away from zero this is eight to the left of zero this is eight to the right of zero so both of these things evaluate to eight absolute value of negative eight is eight absolute value of 8 is 8 and so clearly eight is equal to eight let me do a couple of more examples let's say I had I wanted to compare the absolute value of negative one and I want to compare that to positive two so the absolute value of negative one is just the positive version of one which is it's just a positive version of negative 1 which is just which is just 1 so 1 is clearly less than 2 or the other way to think about it the absolute value of negative 1 is clearly less than 2