1
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2
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We're told to plot these values on a number line.

3
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And you see every one of these values have an

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absolute value sign.

5
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So let's take a little bit of a review of what absolute

6
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value even is.

7
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8
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The way I think about it, there's two ways

9
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to think about it.

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The first way to think about it is, how far is

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something from 0?

12
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So let me plot this negative 3 here.

13
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So let me do a number line.

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This isn't the number line for our actual answer, or to this

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command-- plot these values on a number line.

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I'm just first going to plot the numbers inside the

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absolute value sign, and then we're going to take the

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absolute value and plot those, just like they're

19
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asking us to do.

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So on this number line, if this is 0, if we go to the

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negative, we're going to go to the left of 0.

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So this is negative 1, negative 2, negative 3.

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Negative 3 sits right over there, so this is negative 3

24
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right there.

25
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The absolute value of negative 3 is essentially saying, how

26
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far are you away from 0?

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How far is negative 3 from 0?

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And you say, well, it's 1, 2, 3 away from 0.

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So you'd say that the absolute value of negative 3 is equal

30
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to positive 3.

31
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Now that's really the conceptual way to imagine

32
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absolute value.

33
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How far are you away from 0?

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But the easy way to calculate absolute value signs, if you

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don't care too much about the concept, is whether it's

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negative or positive, the absolute value of it's always

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going to be positive.

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Absolute value of negative 3 is positive 3.

39
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Absolute value of positive 3 is still positive 3.

40
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So you're always going to get the positive version of the

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number, so to speak.

42
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But conceptualy, you're just saying how far away

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are you from 0.

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So let's do what they asked.

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So that first value, on this number line, so all of these

46
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are absolute values.

47
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So they're all going to be positive values.

48
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So they're all going to be greater than 0.

49
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So let me draw my number line, like this.

50
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I can do a straighter number line than that.

51
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Let's see.

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Well, that's a little bit straighter.

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And let's say, if this is 0, this would be negative 1, then

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you'd have 1, 2, 3, 4, 5, 6, 7.

55
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I think that'll do the trick.

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So this first quantity here-- I'll do it in orange --the

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absolute value of negative 3, we just figured out, that is

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positive 3.

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So I'll plot it right over there, positive 3.

60
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Then this next value, right here, the absolute value of 7.

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If we look over here, 1, 2, 3, 4, 5, 6, 7.

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7 is how far away from 0?

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It is 7 away from 0.

64
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So the absolute value of 7 is equal to 7.

65
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So you already see the pattern there.

66
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If it's negative, it just becomes positive.

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If it's already positive, it just equals itself.

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So plotting this value, I'll just place

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it right over there.

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So the absolute value of 7 is 7.

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Absolute value of negative 3 is positive 3.

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Let me mark out the 0 a little bit better, so you see

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relative to 0.

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00:03:22,830 --> 00:03:29,620
Now we have the absolute value of 8 minus 12.

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Well, first of all, let's figure out what 8 minus 12 is.

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So if you take 12 away from 8, you're at negative 4.

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12 less than 8 is negative 4.

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And you can do that on a number line if you don't quite

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remember how to do this.

80
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But if you, you know, if you take 8 away from 8, you're at

81
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0, and then you take another one, you're at negative 1,

82
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negative 2, negative 3, all the way to negative 4.

83
00:03:55,219 --> 00:03:59,580
So this is equal to the absolute value of negative 4.

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If we just plot negative 4, we go 1, 2, 3, negative 4 is

85
00:04:05,439 --> 00:04:06,550
right over there.

86
00:04:06,550 --> 00:04:09,120
But if we're taking its absolute value, we're saying

87
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how far is negative 4 from 0?

88
00:04:11,949 --> 00:04:13,909
Well it's 4 away from 0.

89
00:04:13,909 --> 00:04:16,219
1, 2, 3, 4.

90
00:04:16,220 --> 00:04:18,779
So this is equal to positive 4.

91
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So we'll plot it right here.

92
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This number line is the answer to this command up here.

93
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So the absolute value of 8 minus 12, which is negative 4,

94
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is positive 4.

95
00:04:31,689 --> 00:04:34,959
Then we have the absolute value of 0.

96
00:04:34,959 --> 00:04:37,659


97
00:04:37,660 --> 00:04:40,650
So how far is 0 from 0?

98
00:04:40,649 --> 00:04:42,589
Well, it's 0 away from 0.

99
00:04:42,589 --> 00:04:47,859
The absolute value of 0 is 0, so you can just plot it right

100
00:04:47,860 --> 00:04:48,780
over there.

101
00:04:48,779 --> 00:04:49,959
And we have one left.

102
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Let me pick a suitable color here.

103
00:04:53,189 --> 00:04:56,050
The absolute value of 7 minus 2.

104
00:04:56,050 --> 00:04:59,540


105
00:04:59,540 --> 00:05:02,170
Well, 7 minus 2 is 5, so this is the same thing as the

106
00:05:02,170 --> 00:05:04,379
absolute value of 5.

107
00:05:04,379 --> 00:05:06,654
How far is 5 away from 0?

108
00:05:06,654 --> 00:05:08,869
Well, it's just 5 away.

109
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It's almost, you know, too easy.

110
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That's what makes it confusing.

111
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If I were to plot 5, it's 1, 2, 3, 4, 5.

112
00:05:15,329 --> 00:05:18,709
It is 1, 2, 3, 4, 5 spaces from 0.

113
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So the absolute value of 5 is 5.

114
00:05:21,310 --> 00:05:24,420
So you plot it just like that.

115
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So conceptually, it's how far you are away from 0.

116
00:05:27,300 --> 00:05:29,620
But if you think about it in kind of just very simple

117
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terms, if it's a negative number, it becomes a positive

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version of it.

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If it's a positive number already, it just equals itself

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when you take the absolute value.

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