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Comparing absolute values on the number line

CCSS.Math: ,

Video transcript

what I have here are three numbers plotted on the number line we have the number a the number C the number B and then we have three inequality of four inequalities actually four inequalities that involve absolute value and what I want to do is figure out which of these inequalities are true given where a C and B are on the number line and I encourage you to pause the video and try to think through it on your own alright let's look at this first one it says that a is less than B so if we look at a and we look at B a is clearly to the left of B on the number line so we know that this is this is true even more we know that a is negative it's to the left of zero while B is positive which is if one thing is negative and the other thing is positive the negative thing is definitely going to be less than the positive thing but even easier than that a is to the left of B on the number line if you're to the left of something else on the number line you're less than that other thing because then the number line at least the way we've constructed it it increases from left to right all right the next statement the absolute value of a is greater than the absolute value of B let's just think about where these are on the number line so we've already said a is three hash marks to the left of zero that is a so what is going to be the absolute value of a well the absolute value of a is the distance that a is from zero so the distance that a is from zero is one two three hash marks so the absolute value of a is just going to be that same distance on the positive side so the point that we marked as C is also the absolute value of a so that is also the absolute value of a absolute value of a I'm sorry a is three to the left of zero absolute value of a is going to be three to the right it's just a measure of how how many hash marks is it from zero what's three hash marks from zero so we put it right over here so is the absolute value of a greater than the absolute value of B well what's the absolute value of B well B is one two three four five six seven eight hash marks to the right of zero and so the absolute value of B is going to be on the eighth hash mark because it's eight hash marks to the right so this is also the absolute value of B and this is consistent with what we've learned about absolute value absolute value of a positive number it's just going to be that number again absolute value of a negative number is going to be the opposite of that number an absolute value of zero is just going to be zero so is the absolute value of eight greater than the absolute value of B well no absolute value of a is to the left of the absolute value of B on our number line it is less than the absolute value of B so this is not true all right next statement absolute value of a is less than the absolute value of C well we already know that the absolute value of a is the same value as C so what's the absolute value of C well the absolute value of a positive number is just going to be that number so this this point right over here is also the absolute value of C so we see that the absolute value of a is equal to the absolute value of C it's not less than so we are going to rock we're going to mark that off we could have written absolute value of a is equal to absolute value of C that would have been true all right last one a is less than C well once again a is to the left of C on the number line so that is true because our number line is increasing as we go from left to right if one number is to the left of another number it is less than the other number so a is indeed less than C and we are done