absolute

6 Absolute Value

So both of these things evaluate to 8.

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

Let's do a couple more examples.

So let's say that we wanted to compare the absolute value of 2 to the absolute value of 3.

But if you had some negative numbers here, you would actually say the absolute value of numerator is lesser than the absolute value of the denominator, for a proper fraction

1 Absolute Value Smallest

6 Absolute Value Last

Let's do a couple more of these.

Shift to the right you get minus 1 times 2 plus 2 times 1 to zero.

I know your gut reaction is the natural log of y, which is correct, but there's actually a slightly broader function than that, whose derivative is actually 1 over y, and that's the natural log of the absolute value of y.

So it's 5 times the absolute value of 2 minus 3.

Now, you could integrate both sides of this, and you'll get the natural log of the absolute value of x is equal to the natural log of the absolute value of mu, et cetera, et cetera.

So that first value, on this number line, so all of these are absolute values.

Absolute value of 10. or the absolute value of x, when x 10.

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

2 times 8 is 16, minus 5 gives 11.

2 times negative 3 is negative 6, minus 5 gives negative 11.

So you take negative 2 here.

So this is going to be equal to the ( abs( 15) abs( 46) abs( 29)) and the reason why we are writing this. this might look fancy but this is really just the length of this purple arrow.

Because here, that obviously works for positive values, because the absolute value of x will be equal to x.

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So let's think about these numbers.

So, let's just think about absolute value of x, when x 5.

We have some f of x less than a.

That's 2.

Or it could be less than negative 5 7, because if it's

So they're all going to be positive values.

I'll just place it right over there.

So the absolute value of 7 is 7.

This guy, he knows that his number is either 20 plus a, or the absolute value of 20 minus a.

Because if this is equal to 11, the absolute value of 11 is 11,

The absolute value of x, when x 12.

If x is equal to negative 5, same drill.

So the absolute value is 15.

And we get 100 over here, which is minus 100 over here plus zero, which gives minus 100.

If the absoulte value of 2x minus 5 is equal to 11 that means that the stuff inside the absolute value sign either equals 11 or the stuff inside the absolute value sign is equal to NEGATlVE 11.

I'm definitely not going back home!

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

You get 2 times 0, which is 0, minus 3 and 1 4.

So in general absolute value will always be a positive quantity.

So it also has to be greater than negative 7 and 1 2.

It's either a positive number or 0.

It is 7 away from 0.