1) The document provides class notes and work on solving absolute value equations. It gives the steps to solve an absolute value equation: split it into two equations, one with the absolute value and one with the opposite, then solve each individually. 2) An example problem walks through solving |x - 1| = 3, getting solutions of x = 4 and x = -2. 3) The last problem asks the distance between the highest and lowest elevations in North America, Mt. McKinley at 20,320 feet and Death Valley at -282 feet.

1. Friday, September 27, 2013
Today:
Make-Up Tests Now
Warm-Up
Absolute Value Equations
Khan Academy Due Sunday: 7:00 pm
Class work:

2. Warm-Up (5); fr. Test
Version 1
1) .3x + .3 = .6x + .7 - .5x A) .32 B) 15 C) 2 D) .4 E) None
Version 2
Version 3
9) The first stage of a rocket burns 28 seconds longer than the second
stage. If the total burning time for both stages is 182 seconds, how
many seconds does the first stage burn for?
A) 124 B) 77 C) 98 D) 90 E) 105

3. Absolute Value
0 5-5 10-10
10 10

4. Absolute Value
0 5-5 10-10

5. Solving Absolute Value Equations
To solve (when the absolute
value is by itself), split into two
equations:
• One with a positive 3x
• The other with the opposite of
3x = 6
Then solve each individually
What are x = 2; x = -2
Because the |x|could be positive or
negative, (why)we must solve for
both possibilities.

6. Check for Understanding
What is the solution to |3x + 1| = - 5
There is no solution. The result of an absolute equation
can never be negative.
But what about the second equation that we write using
a negative sign? The difference is:
The original equation is always a positive. For example,
|3x + 1| = 5
If the original absolute value equation equals a
negative number, there is no solution.

7. Guided Practice
Ex.1: 3|x - 1| + 1 = 10
For the Positive Value:
1. Goal: Isolate the absolute value
a. Subtract 1
b. Divide by 3
c. add 1. x = 4
3|x - 1| + 1 = 10
- 1 - 1
3|x - 1| = 9
|x - 1| = 3
x = 4
3|x - 1| + 1 = 10
- 1 - 1
3|x - 1| = 9
-x + 1 = 3
-x = 2; x = -2
For the Negative Value:
1. Goal: Take the opposite of
the absolute value
2. a. Subtract 1
b. Divide by 3
c. Take the opposite of the
ab. value
d. add 1; x = -2
Plug in and check each value!!!!

8. Summary
What are the steps to solve an absolute value equation?
1. Is the Absolute Value alone (isolated) on one side?
2. Split the Absolute Value into two equations
3. One equation takes the absolute value, one takes the
opposite of the absolute value
4. Solve each equation individually
5. Check your answers by plugging them in!

9. Absolute Value
4. |x + 6| + 12 = 18
Solve for the positive first
b. Subtract 6 from each side. x = ?
Goal: Get the absolute value by itself on the left side.
a. Subtract 12 from each side
0

10. Warm-Up
Solve for the negative next
Goal: Get the absolute value by itself on the left side
before taking the opposite:
a. Subtract 12 from each side
b. We have |x + 6|= 6; Now we can change the
equation to: -|x + 6|, or -x - 6 = 6; -x = 12; x = -12
The solutions are x = 0, or x = -12
Absolute Value
e. Plug in each value. Are both -4 & -8 solutions?

11. Absolute Value: Last Problem
The highest elevation in North
America is Mt. McKinley,
which is 20,320 feet above sea
level. The lowest elevation is
Death Valley, which is 282 feet
below sea level. What is the
distance from the top of Mt.
McKinley to the bottom of
Death Valley?

12. Class Work: Handout: Please use
separate page for NUMBERED
scratch paper.