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## Grade 7 (Virginia)

### Course: Grade 7 (Virginia) > Unit 1

Lesson 5: Absolute value- Comparing absolute values on the number line
- Placing absolute values on the number line
- Comparing absolute values
- Compare and order absolute values
- Absolute value as distance between numbers
- Interpreting absolute value as distance
- Absolute value to find distance

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# Comparing absolute values on the number line

Given, a, b, and c on the number line, Sal determines if statements like | a | < | c | are true.

## Want to join the conversation?

- Did Sal actually say " the number "b"?(13 votes)
- Yes, he even said that to A and C.(0 votes)

- the number b taste good(3 votes)
- What do you mean!?!? 0-0…(1 vote)

- No one noticed that the colors he's using for the numbers on the Number line are the pansexual flag colors-(3 votes)
- i did not even see the number line-(2 votes)

- I Watched it it it still says not finished(2 votes)
- You have to watch a certain amount of the video to complete it. If you skip the video enough then it wont finish, just watch it again some more(1 vote)

- why did you use letters instead of numbers because I never saw that before in my life? And how do you know what is negative and positive? I am so confused right now(2 votes)
- Letters are used as variables, for an unknown number.(1 vote)

- the absolute value of A is 3 right?(1 vote)
- The absolute value A could be 3, but it also could be any other value. Since the hash marks aren't labelled, we don't know the value that they represent.

All we know is that a hash mark is equal to 1/3 the value of c (c/3).

Sorry if this is confusing, it will make more sense when you learn about variables.(1 vote)

- Sal said all the letters as a number at0:04(1 vote)
- The letters are variables to fill in unknown numbers, so probably that's why.(1 vote)

- It depends on what you mean by the question. Anything inside the absolute value sign will always come out non-negative (positive or 0), but the answer does not always have to be positive. We could invert the absolute value y = - |x| where all the answers are negative, we could shift the absolute value equation down such as y = |x| - 4 where all the values of x such that -4<x<4 would be negative.(1 vote)
- How do we use absolute value to help solve problems in the real world (ex. agriculture, engineering, transportation)?(4 votes)
- say you have a starting point (0) you could see the exact point of wherever that number came from and what it is(0 votes)

## Video transcript

- [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.