1. Today
Thursday's Khan Report: 1506 minutes!!!
(25.1 hrs)
Khan Academy Info.
Equation Practice
Including Absolute Value

2. Checking Your Progress
How to tell whether you've completed a topic:
1. Go to 'Your Profile' 2. Select 'Skills Progress'

3. Checking Your Progress
Hold mouse over any red or light blue
topic. You will see your progress percent.
100% = 8 or more consecutive questions
answered correctly

4. Checking Your Progress
Double clicking the topic will open the
following window:

5. Class Notes:
Absolute Value Equations

6. Absolute Value
10 10
-10 -5 0 5 10

7. Absolute Value
-10 -5 0 5 10

8. Solving Absolute Value
To solve (when the
absolute value is by
itself), split into two
equations:
• One with a positive 6
• The other with a
negative 6
Then solve each
individually

9. 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? There are 2 differences. 1st: The original
equation is always a positive. For example, |3x + 1| = 5
2nd: Given |3x + 1| = 5, the second equation is really written as:
- |3x + 1| = 5; The opposite of the absolute value....
So, the opposite of -|3x - 1| = 5; Therefore, -3x = 6; -3x/-3 = 6/-3; x = 2
Our shortcut is to put the negative on the other side, because
it works out the same. If the original absolute value equation
equals a negative number, there is no solution.

10. Guided Practice
Ex.1: 3|x - 1| + 1 = 10 For the Positive Value:
3|x - 1| + 1 = 10 1. Goal: Isolate the
-1 -1 absolute value
3|x - 1| = 9 a. Subtract 1
|x - 1| = 3 b. Divide by 3
x=4 c. add 1. x = 4
For the Negative Value:
3|x - 1| + 1 = 10
1. Goal: Isolate the absolute
-1 -1
value
3|x - 1| = 9
a. Subtract 1
|x - 1| = -3
b. Divide by 3
x = -2
c. Then Change sign to
negative
d. add 1; x = -2

11. 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. Change the sign on the right only after isolating
the absolute value.
4. Solve each equation individually
5.Check your answers by plugging them in!

12. Warm-Up
Emergency Khan Academy Questions:
Combining Like Terms with Distribution

13. Warm-Up
Equations: Build from the ground up
1. Write and solve an equation with distribution.
2. Write and solve an equation with distribution
and a variable on each side. The answer must be a
whole number.
Absolute Value
3. |x/5| = 2 3. |x/5| = 2; |x/5| = - 2

14. Warm-Up
4. 3|x + 6| + 12 = 18
Solve for the positive first
Goal: Get the absolute value by itself on the
left side.
a. Subtract 12 from each side b. divide by
3 c. Subtract 6 from each side -4 d. x =
? Solve for the opposite next
Goal: Get the absolute value by itself on the
left side before changing the sign on the right
side.
a. Subtract 12 from each side b. divide by 3
c. We have |x + 6| = 2; Now we can change the
equation to: x + 6 = -2
d. Solving, we get x = 2. The solution is x = - 4, or x =
-8

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