1. Absolute Value Equations

2. Absolute Value Review Integers have two components: A value – shows how far a number is from zero A direction – the sign shows which side of zero Positive Integers are to the right of zero Negative Integers are to the left of zero Absolute Value is the distance from zero – direction doesn’t matter

3. Do you remember this? What if you had this? What two numbers could “x” be to give you this answer of 5 ?

4. 2) | x + 2 | = 10 So, ultimately, what would have to be between the absolute value bars to give me an answer of 10? Now to find the value of “x”, set up 2 equations using the information found between the absolute value bars….. One for the NEGATIVE And one for the POSITIVE

5. 3) | x – 6 | = 13 Now to find the value of “x”, set up 2 equations using the information found between the absolute value bars….. One for the NEGATIVE And one for the POSITIVE So, ultimately, what would have to be between the absolute value bars to give me an answer of 13?

6. Now find the value of “x”, set up 2 equations using the information found between the absolute value bars….. One for the NEGATIVE And one for the POSITIVE Now what 2 numbers Will give us 12?

7. This problem has an extra term outside the bars. You must first eliminate any extra terms. Now set up your 2 problems The NEGATIVE side And the POSITIVE side

8. This problem has an extra term outside the bars. You must first eliminate any extra terms. Now set up your 2 problems The NEGATIVE side And the POSITIVE side

9. Eliminate extra terms first!! Now you CAN’T set up your 2 problems INVALID EQUATIONS When you have absolute value bars on one side of an equation and a constant on the other side, the constant can NEVER be NEGATIVE

10. Don’t forget to eliminate all extra terms first!!! Now set up your 2 problems The NEGATIVE side And the POSITIVE side

11. Don’t forget to eliminate all extra terms first!!!! Now set up your 2 problems The NEGATIVE side And the POSITIVE side

12. Sum, Product, Difference and Quotient. What is the sum of the solutions for example #2? What is the product of the solutions for example #4? What is the sum of the solutions for example #3 What is the product of the solutions for example #9 Use the answers to the previous examples for the following.