Review on solving inequalities from College Algebra

**Qudadratic Inequalities**

Type I. Standard Form (coefficients of *x* are positive and the degree of
each factor is 1.)

Example: Solve (*x*-2)(3*x*+1)<0. We get two points and 2 on
the real line as if we have equality, and we alternate + and - from the
right to the left, so our answer to this question is

Type II. Non-Standard Form, but can be made standard by multiplying ''negative(s)''.

Example: Solve (-*x*-2)(3*x*+1)<0, this is not in standard form, but we can
multiply (-*x*-2) by -1, which yields, (*x*+2)(3*x*+1)>0. So the solution
will be

Type III. Can't be made standard, needs to use a table

Example: Solve (3*x*+1)^{2}(*x*-2)(*x*-3)<0. First we get and 3.
Next we complete the following table: Therefore the answer is (2,3).

Example: Solve According the table above, the answer will be or

**Fractional Inequalities**

Example: Solve This is equivalent to solve (*x*-1)(*x*-3)(*x*-5)>0. We know that we can apply the ''standard form''
technique to do this one.

Example: Solve This is equivalent to solve (*x*-1)^{2}(*x*-3)(*x*-5)>0 and we can make a table to solve this problem.