1. 4.4 – Solving Absolute Value Equations

2. Absolute Value = denoted by |x|, is the distant a number is from zero Always a positive number! (or zero)

3. Absolute value equations are equations with one, or more, absolute value terms We will use the idea that a number is a distance from zero in order to solve What are two numbers with an absolute value of 8?

4. Solving For the absolute value equation, |ax + b| = c, where c > 0, The solutions to solve for are; ax + b = c ax + b = -c Why?

5. Important! Just as before, we need to check our solutions! Plug back into the original absolute value equation

6. Example. Solve the absolute value equation |5x – 2x| = 9

7. Example. Solve the absolute value equation |1 – 2x| = 9

8. If the absolute value term is not isolated, isolate like we were isolating the particular variable Example. Solve the absolute value equation |3x + 6| + 4 = -4

9. Example. Solve the absolute value equation |4x – 3| - 1 = 2

10. Example. Solve the absolute value equation |x + 5| = -5 Problem?

11. Example. In an applied sense, absolute value equations may be used when we have a max and min value. For example, in Tallahassee, the equation for temperature for record high and low is given by |x – 55.5| = 49.5, degrees Fahrenheit. Find the highest and lowest temperatures recorded in Tallahassee.

12. Assignment Pg. 195 3-11 odd, 25-32 all, 37, 38, 59b, 59c