1. 6.5 Solving Open Sentences involving Absolute Value
Remember the absolute value is the distance from zero on a number line.
Absolute value means you are going to have 2 equations!
The expression inside the absolute value symbols is either positive or negative.
|x – 4| = 5
Write the equation without the absolute values and then again with the other sign after the =.
x – 4 = 5 OR x – 4 = -5
Solve.
x = 9 or x = -1
Solution is {-1,9}

2. Try These Solve |b + 6| = 3 {-9, –3}
You may get the answer and be asked for the equation!
Find the middle between the 2 numbers. 1
How many spaces did you move to get there? 5
Plug that information into an equation:
|x – middle| = spaces you moved to get there
|x – 1| = 5 1 6 -4

3. Try this one Write the equation for this graph. What is the middle #?12
How many spaces did you move to get there? 5
Plug it into the equation
|x – 12| = 5 17 7 12

4. Graphing absolute value functions
An absolute value function is a function written as f(x) = |x| when f(x) > 0 for all values of x.
It’s sometimes known as a piecewise function: a function that can be written using two or more “pieces” or expressions.
Think V for Value!!!

5. Try This One Graph f(x) = |x – 4| Set x – 4 = 0 x = 4
The V-point (4,0)
Slope is 1 to the right of (4,0) (positive) x - 4
Slope is –1 to left of (4,0) (negative) –x + 4

6. Homework
p Check them with me before you begin your homework.
#42 p odd, 47, 49-51