Absolute value examples

Find the absolute value of x when x is equal to 5, x is equal to negative 10, and x is equal to negative 12. So the absolute value, the way of writing it is almost more complicated than what it really is. The absolute value is really just the distance of x from 0. So let me just draw a fast number line over here. So let's just put 0 right over here, since we're thinking about the distance from 0. So let's just think about the absolute value. Let's think about the absolute value of x when x is equal to 5. So that's equivalent to the absolute value of 5. We just substituted 5 for x. The absolute value of 5 is the distance of 5 from the 0. So you go 1, 2, 3, 4, 5. 5 is exactly 5 to the right of 0. So the absolute value of 5 is just 5. Now I think you already get to see this is a pretty straightforward concept. Now let's do something a little more interesting, the absolute value of x when x is equal to negative 10. So let's just put negative 10 in for x. This is the distance that negative 10 is from 0. And so let's just go negative 1, negative 2, negative 3, negative 4, negative 5, negative 6, negative 7, negative 8, negative 9, negative 10. I should extend the number line more. So this right here is negative 10. So how far is it away from 0? Well, it's 10 to the left of 0. So you put a 10 here. And so in general, absolute value will always be a positive quantity. And when we're rethinking about just absolute values of just numbers, it's just going to be, really, the positive version of that number. Let's do one more. Well, they tell us to do one more, the absolute value of x when x is equal to negative 12. So we have the absolute value of negative 12. We don't even to look at the number line. It's just going to be the positive version of negative 12. It's just going to be equal to 12. And this is just saying that negative 12 is 12 away from 0. And we could draw it over here. This is negative 11. Negative 12 is right over here. It is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 away from 0.