00:01
Number of heads that would establish the clueling as being unfair by solving this absolute inequality for h.
00:11
Now if the absolute value of this quantity is greater than or equal to 1 .645, that means this quantity could be greater than or equal to 1 .645, or we have to also consider that this quantity could be less than or equal to negative 1 .645.
00:33
Because if h minus 50 over 5 is less than or equal to negative 1 .645, then the absolute value will make it greater than or equal to 1 .645.
00:47
So we're going to write that two ways.
00:50
Either h minus 50 over 5 is greater than or equal to 1 .645.
00:59
645.
01:02
We'll solve this inequality for h or h minus 50 over 5.
01:15
As we said, h minus 50 over 5 could be less than or equal to negative 1 .645.
01:29
All right.
01:30
If this is positive, then it's easy to see that h minus 50 over 5 would have to be greater than or equal to 1 .645.
01:37
But if this is negative, okay, this is the case where it's negative.
01:42
If h minus 50 over 5 is negative, then if it's less than or equal to negative 1 .645, the absolute value will make it greater than or equal to positive 1 .645.
01:53
Let me just give an example so it kind of makes sense.
01:56
Let's suppose that h minus 50 over 5 was negative 2.
02:04
Well, negative 2 is less than or equal to negative 1 .645.
02:09
But if this was negative 2, the absolute value of negative 2 would be positive 2 and positive 2 of course would be greater than or equal to positive 1 .645.
02:20
So these are the two situations we get from this absolute value inequality and we need to satisfy, we need to solve both of these.
02:29
So look at case 1, where h minus 50 over 5 is greater than or equal to 1 .645, multiplying both sides.
02:39
Of the inequality by positive 5.
02:44
Well, 1 .645 times 5 comes out to be 8 .225.
03:04
And then adding 50 to both sides gives us h is greater than or equal to 58 .225...