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Let's do some examples comparing absolute values.

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So, let's say we were to ask ourselves

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how -9, the absolute value of -9 I should say,

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how that compares to the absolute value of

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-let me think of a good number--the absolute value of -7.

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So, let's think about this a little bit and

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let's think about what -9 looks like or

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where it is in the number line and

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where -7 is on the number line.

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Let's see where the absolute values mean and

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then we should probably be able to do this comparison.

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So there are a couple ways to think about it.

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One is you can draw them on the number line.

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So, if this is 0 and this is -7

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and then this is -9 right over here.

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Now when you take the absolute value of a number,

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you are really saying how far is that number from 0,

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whether it is to the left or the right of 0.

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So for example, -9 is 9 to the left of 0.

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So the absolute value of -9 is exactly 9.

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This evaluates to 9. -7 is exactly 7 to the left of 0.

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So the absolute value of -7 is +7.

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And so, if you were to compare 9 and 7

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then this is a little bit more straight forward.

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9 is clearly greater than 7.

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And if you ever get confused with the greater than and less than symbols,

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just remember that the symbol is larger on the left hand side,

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so that is the greater than side.

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If I were to write this, and this is actually also a true statement.

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If you took this without the absolute value signs,

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it is also true that -9 is less than -7.

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Notice the smaller side is on the smaller number.

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And so that is the interesting thing: -9 is less than -7

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but their absolute values, since -9 is further to the left of 0,

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it is the absolute value of -9 , which is 9,

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is greater than the absolute value of -7.

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Another way to think about it is

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if you take the absolute value of a number,

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it really is just the positive value of that number.

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So if you took the absolute value of 9 that equals 9.

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Or the absolute value of -9, that is also equal to 9.

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When you think of it visually, that is

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because both of these numbers are exactly 9 away from 0.

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This is 9 to the right of 0 and this is 9 to the left of 0.

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Let's do a few more of these.

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So let's say that we wanted to compare

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the absolute value of 2 to the absolute value of 3.

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Well the absolute value of a positive is just going to be that same value.

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2 is 2 to the right of 0. So this is just going to evaluate to 2.

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And then the absolute value of 3,

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that is just going to evaluate to 3.

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That is actually pretty straight forward.

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So 2 is clearly the smaller number here

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so we clearly get 2 is less than 3.

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Or the absolute value of 2 is less than 3.

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So we have a less than right over here.

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Let's say you wanted to compare

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-I am trying to find a suitable color-

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the absolute value of -8 to the absolute value of 8.

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One way to think about it is that they are both 8 away from 0.

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This is 8 to the left of 0 and this 8 to the right of 0.

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So both of these things evaluate to 8.

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Absolute value of negative 8 is 8 and absolute value of 8 is 8.

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So clearly 8 is equal to 8.

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Let's do a couple more examples.

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Let's say that I wanted to compare the absolute value of -1 and

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I want to compare that to +2.

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So the absolute value of -1 is just positive version of -1 which is just 1.

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So 1 is clearly less than 2.

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Or, the other way to think about it is

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the absolute value of negative 1 is clearly less than 2.