Question 719218
{{{ (-(x-1)^2(2-x))/((3-x)(5x-1)^2)>=0 }}}
**
critical points:
x=1 (multiplicity 2)
x=2
x=3
x=1/5 (multiplicity 2)
Draw a number line with critical points on it:
<....-...1/5...-....1....-.....2...+.....3.....-.....>
Explanation:
When x>3, the expression becomes positive, but the negative sign in front makes it negative instead.
Going thru each critical point to the left, the intervals switch signs for odd multiplicities like 1,3, etc, but do not switch when going thru even multiplicities like 2,4, etc.
Solution: [2,3] (this is the only interval where x-values make the expression &#8805;0)
You could also do this with a chart but is is a much longer and tedious process.