# Solutions to the Problems on Absolute Value Inequalities

Math 101

7-20-2012

1. Solve the inequality . Write your answer using either inequality notation or interval notation. Show your work!

Since the " " is on the "big" side of the " ", the solution will be the outer intervals:

Find the break points by solving the corresponding equality:

Write down the inequality for the shaded region. The solution is or . In interval notation, this is .

2. Solve the inequality . Write your answer using either inequality notation or interval notation. Show your work!

Since the " " is on the "small" side of the " ", the solution will be the inner interval:

Find the break points by solving the corresponding equality:

Write down the inequality for the shaded region. The solution is . In interval notation, this is .

3. Solve the inequality . Write your answer using either inequality notation or interval notation. Show your work!

Since the " " is on the "big" side of the " ", the solution will be the outer intervals:

Find the break points by solving the corresponding equality:

Write down the inequality for the shaded region. The solution is or . In interval notation, this is .

4. Solve the inequality . Write your answer using either inequality notation or interval notation. Show your work!

Since the " " is on the "small" side of the " ", the solution will be the inner interval:

Find the break points by solving the corresponding equality:

Write down the inequality for the shaded region. The solution is . In interval notation, this is .

5. Solve the inequality . Write your answer using either inequality notation or interval notation. Show your work!

The absolute value of a number can't be negative, so can't be less than -30. Hence, there are no solutions.

6. Solve the inequality . Write your answer using either inequality notation or interval notation. Show your work!

Since the " " is on the "big" side of the " ", the solution will be the outer intervals:

Find the break points by solving the corresponding equality:

Write down the inequality for the shaded region. The solution is or . In interval notation, this is .

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