**Solving Polynomial and Rational Inequalities**

.

**Sol 1** Factoring gives
or . Marking 0,3, and
-2 on a number line, and using that

and that all the
exponents are odd, we get the sign chart shown below:

Therefore the solution is given by .

**Sol 2** Factoring gives or .
Marking 0,3, and -2 on a number line, and using that

and that the sign changes at 3
and -2 but does not change at 0, we get the sign
chart shown below:

Therefore the solution is given by .

**Sol 3** Factoring gives

and marking 4,1,2, and -2 on a number line, and using that

and that all the exponents are
odd, we get the sign chart shown below:

Since the inequality is not strict, we can include the zeros of the numerator; so the solution is given by .

**Sol 4** Factoring gives

and marking 5/2,-2, 4, and -3 on a number line, and using that

and that all the exponents are
odd, we get the
sign chart shown below:

Therefore the solution is given by .

**Sol 5** Factoring gives

or

Marking -3,-2,-1,1,2, and 3 on a number line, and using the facts that

and that all the exponents are
odd, we get the following sign chart:

Since the inequality is not strict, we can include the zeros of the numerator; so the solution is given by .

**Sol 6** Since for all , and therefore for all ; so multiplying by gives the equivalent
inequality .

Factoring yields or ; so marking on a number line and using that

when and all the
exponents are odd,
we get the following sign chart:

Therefore the solution is given by .

**Sol 7** Factoring gives the inequality

or

Marking off -2,0,1/3,1,3/2, and 4, and using the facts that

and the sign
changes at
3/2,1,-2, and 1/3 and does not change at 0 or at 4, we get the
following sign chart:

Since the inequality is not strict, we can include the zeros of the
numerator;
so the solution is given by
.

Correction: the
solution should include x=0 as well.

**Sol 8** Subtracting from both sides
gives , so or .

Marking -4,0,and 4 on a number line, and using that

and that all the exponents are
odd, we get the following sign chart:

Therefore is the solution.

**Sol 9** Subtracting from both sides gives

so

Therefore

so

or

Marking 2,4, and -1 on a number line, and using the facts that

and that all the exponents are
odd, we get the
following sign chart:

Therefore is the solution.

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