00:01
So we're given this inequality, and we're going to try and find the solution set interval, and we're going to put it in interval notation.
00:08
So what i'm going to do is i'm going to first find the zeros of our inequality.
00:13
So in this case, since we have a negative x squared multiplied by everything, we're going to have a zero at x is equal to zero, and we're going to have a zero where 2x minus 3 is equal to 0.
00:26
So if we solve this, we get 2x is equal to 3, so x is equal to 3.
00:30
Equal to 3 over 2 and we can see if we plug in 3 over 2 2 2 times 3 over 2 is 3 minus 3 is 0 and multiplied by whatever our negative x squared is is also going to be 0 so these are the 2 zeros of our function and now that we know these 2 zeros what we want to do is look at the intervals from negative infinity to 0 and then from 0 to 3 halves and then from three halves to infinity.
01:03
And we're going to see if our solution is actually going to be less than or equal to zero by just looking at the sign of our solution on these intervals.
01:12
So another way to write this inequality is to make it a little bit less confusing.
01:17
I'm just going to rewrite it as negative x squared times 2x minus 3 squared as less than or equal to 0...