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Find the absolute value[br]of x when x is equal to 5,

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x is equal to negative 10,[br]and x is equal to negative 12.

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So the absolute value,[br]the way of writing it

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is almost more complicated[br]than what it really is.

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The absolute value is really[br]just the distance of x from 0.

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So let me just draw a fast[br]number line over here.

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So let's just put[br]0 right over here,

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since we're thinking[br]about the distance from 0.

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So let's just think[br]about the absolute value.

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Let's think about[br]the absolute value

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of x when x is equal to 5.

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So that's equivalent to[br]the absolute value of 5.

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We just substituted 5 for x.

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The absolute value of 5 is[br]the distance of 5 from the 0.

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So you go 1, 2, 3, 4, 5.

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5 is exactly 5 to[br]the right of 0.

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So the absolute[br]value of 5 is just 5.

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Now I think you[br]already get to see

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this is a pretty[br]straightforward concept.

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Now let's do something a[br]little more interesting,

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the absolute value of x when[br]x is equal to negative 10.

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So let's just put[br]negative 10 in for x.

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This is the distance that[br]negative 10 is from 0.

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And so let's just go negative[br]1, negative 2, negative 3,

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negative 4, negative 5, negative[br]6, negative 7, negative 8,

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negative 9, negative 10.

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I should extend the[br]number line more.

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So this right here[br]is negative 10.

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So how far is it away from 0?

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Well, it's 10 to the left of 0.

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So you put a 10 here.

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And so in general,[br]absolute value

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will always be a[br]positive quantity.

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And when we're rethinking[br]about just absolute values

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of just numbers, it's[br]just going to be,

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really, the positive[br]version of that number.

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Let's do one more.

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Well, they tell us to do one[br]more, the absolute value of x

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when x is equal to negative 12.

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So we have the absolute[br]value of negative 12.

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We don't even to look[br]at the number line.

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It's just going to be[br]the positive version

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of negative 12.

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It's just going[br]to be equal to 12.

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And this is just saying that[br]negative 12 is 12 away from 0.

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And we could draw it over here.

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This is negative 11.

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Negative 12 is right over here.

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It is 1, 2, 3, 4, 5, 6, 7,[br]8, 9, 10, 11, 12 away from 0.