1. Absolute Value Equations and Inequalities

2. Today's questions to answer...
~ What is the absolute value of a number?
~ How do we solve an absolute value equation?
~ How do we solve an absolute value inequality?
~ What are some real-world examples?

3. What is the absolute value of a number?
~The distance the number is from 0 on a number line.
Written as...

4. Quick Example: So, what is the difference between and ?
Determine the value of the following:
So, what is the difference between and ?

5. REMEMBER, THE ABSOLUTE VALUE OF X AND -X ARE THE SAME!
But what will happen when "x"is thrown into the mix?
Suppose we have
*******
where a,b, and c are real numbers and c>0.
REMEMBER, THE ABSOLUTE VALUE OF X AND -X ARE THE SAME!
What does that mean for c?

6. This is how we do it...
When
*******
We solve two problems...

7. Example 1)
Solve
************

8. Try this on your own...
*****

9. Let's change our signs...
For parts a and b, try several numbers for "x"and see if you notice a pattern. a) b)

10. Absolute Value is less thAN...
For
*********************
an "and"compound inequality is created. So, this becomes...
Absolute Value is great"OR" than
For
******
an "or" compound inequality is created. So, this becomes...

11. Example 2)
Solve
Example 3)
Solve

12. Try these on your own... 1) 2)
***

13. Pop Problem!!

14. Example 5)
At the Brooks Graphic Company,the average starting salary for a new graphic designer is $37,600, but the actual salary could differ from the average by as much as $2590.
a) Write an absolute value inequality to describe this situation.
b) Solve the inequality to find the range of starting salaries.

15. Questions?