00:01
How many real solutions are possible for the inequality 500x squared minus x is less than 0? so let's pretend that we don't have a less than sign, and let's pretend there's an equal sign.
00:18
So what we're going to do is we're going to factor this, and we're going to have x come out because that's a common factor.
00:27
And we're going to have 500x minus 1 is equal to 0.
00:31
So here we're going to have x is equal to 0 and 500x minus 1 is equal to 0.
00:40
X therefore is equal to 1 over 500.
00:46
So let's put these into our initial inequality and let's see if they hold true.
00:52
So if we put 0 in, we're going to have 0 is less than 0.
00:58
Well, this is not true.
01:02
0 is equal to 0.
01:04
So let's put in 1 over 500.
01:07
So we have 500 times 1 over 500 squared minus 1 over 500.
01:18
Hundred.
01:20
So when we put this into our calculators, we're going to end up with one over five hundred minus one over five hundred is less than zero, or zero is less than zero.
01:34
And again, we know that's not true.
01:36
Zero is equal to zero.
01:38
So we have our outer limits of our inequality.
01:43
We can't go go outside of these limits.
01:47
So let's try a different one...