How do you solve #(x(x-4))/(2-3x)<= 3#?
Multiplying the numerator by x gives
Multiplying by the denominator gives
For the inequality to be true one term must be positive and the other negative
Rewrite to get a single ratio on the left.
Find the key numbers (partition numbers, unnamed special numbers) for the expression on the left. These are the places where the expression might change sign. We find them by finding the zeros and the places where the expression is undefined.
In the end we solve
The key numbers are:
They cut the real number line into intervals:
We want the value of