Comparing absolute values on the number line

- [Voiceover] 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 -- (laughs) we have four inequalities, actually. Four inequalities that involve absolute value. And what I want to do is figure out which is 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. All right, 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 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 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." Well, 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. The absolute value of a -- 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 many hash marks is it from zero? Well, it'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? Or 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 is just going to be that number again. Absolute value of a negative number is going to be the opposite of that number. And absolute value of zero is just going to be zero. So is the absolute value of a 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 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 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.