# Solutions to Problem Set 31

Math 101-06

11-29-2017

[Inequalities]

1. Solve the following inequality. Write your answer using either inequality notation or interval notation.

Let .

for and .

is defined for all x.

Plug test numbers in , , and into f:

I want the values of x for which is positive. The solution is or . In interval notation, this is .

2. Solve the following inequality. Write your answer using either inequality notation or interval notation.

Let .

for and .

is defined for all x.

Plug test numbers in , , and into f:

I want the values of x for which is negative or equal to 0. The solution is or . In interval notation, this is .

3. Solve the following inequality. Write your answer using either inequality notation or interval notation.

I need to have 0 on one side, so rewrite the inequality as

Let .

for , , and .

is defined for all x.

Plug test numbers in , , , and into f:

I want the values of x for which is negative. The solution is or . In interval notation, this is .

4. Solve the following inequality. Write your answer using either inequality notation or interval notation.

Let .

for .

is undefined for .

Plug test numbers in , , and into f:

I want the values of x for which is negative. The solution is or . In interval notation, this is .

5. Solve the following inequality. Write your answer using either inequality notation or interval notation.

Let .

for and .

is undefined for .

Plug test numbers in , , , and into f:

I want the values of x for which is positive. The solution is or . In interval notation, this is .

6. Solve the following inequality. Write your answer using either inequality notation or interval notation.

Let .

for .

is undefined for and .

Plug test numbers in , , , and into f:

I want the values of x for which is positive. The solution is , , or . In interval notation, this is .

Strength doesn't come from physical capacity. It comes from indomitable will. - Mahatma Gandhi

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