Higher Order and Fractional inequalilities
If it is in standard form or can be transformed into the
standard form, then apply the short cut. Example: Solve (-2x - 1)(-3x
+ 1)(x-5) < 0. We first multiply by (-1) on "-2x -1" and another (-1) on
"-3x + 1", yield (2x + 1)(3x - 1)(x-5) <0 (We don't switch the
inequlality, because we multiply "+ 1".
If a problem can't be transformed into a standard form, then we need
to use "table" to find out the answers. (refer to your notes).
Example: Solve [(2x-1)^2](x - 1)(x-3)(x-5) > 0.
Example: Solve (x-1)/(x-3) > 0. Notice that the signs (+ or -)
of (x-1)/(x-3) are the same as (x-1)(x-3). So whenever we see a
fractional inequality, first transform it into a muliplication inequality
(and be sure that the denominator is not equal to 0). [Answer:
(-infinity, 1) union (3, infinity).]