The document provides information about Khan Academy lessons on the distance formula, absolute value expressions and equations. It includes examples of using the distance formula to calculate average speed. It also provides steps for solving absolute value equations, including isolating the absolute value term, splitting into two equations taking positive and negative values, and finding the solutions. Examples are worked through, and class work is assigned for November 10th involving solving absolute value equations.

1. Today :
 Khan Academy Review
11/06/15
 The Distance Formula
 Begin Class Work 2.2
Absolute Value Expressions & Equations

2. 𝟏𝟓
𝟓
𝟏𝟓
𝟑
The Distance Formula
where r = rate (speed) and t = time

3. If you drive 180 miles in 2 hours, what is your average speed?
How long will it take each car to
travel the 200 miles?
5 hrs.
4 hrs.

4.  An airplane can travel the 1960 miles between
Saipan and Japan in 3.5 hours. What is the average
speed of while in the air?

7.  What are the possible solutions to |x| = 5?
 Because the variable could be negative or positive, all
absolute value equations are solved for BOTH possibilities.
 All absolute value equations have two equations.

8. Steps to solving absolute value equations
3|x| = 15
1. Isolate the Absolute Value on one side of the equation.
|x| = 5
2. Split the Absolute Value into two equations Method 1:
One equation takes the absolute value, x = 5
- x = 5
Once isolated, the absolute value bars can be
removed. x = 5
the other takes the opposite of the absolute value
Our solutions are, x = 5 or x = -5
(Solve each equation individually)

9. Steps to solving absolute value equations
3|x| = 15
1.Isolate the Absolute Value on one side of the equation.
|x| = 5
2. Split the Absolute Value into two equations Method 2:
One equation takes the positive value of the right side of
the equation x = 5
x = - 5
Once isolated, the absolute value bars can be
removed. x = 5
the other takes the negative value
of the right side of the equation:
Our solutions are, x = 5 or x = -5
(I prefer method 2, but the choice is yours)

10. |x + 6| + 12 = 18
Solve for the positive first
b. Subtract 6 from each side. x = ?
Get the absolute value by itself on the left side.
a. Subtract 12 from each side
0
Example 2 of 3

11. 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
e. Plug in each value. Are both -4 & -8 solutions?
|x + 6| + 12 = 18

12. 7 + |2x  4| = 2
A Final Example:
1. Isolate the absolute value on the left
2. |2x  4| = -5
If you look carefully at the above equation, you realize
the statement is impossible, and therefore, the equation
has no solution.
Remember!
Absolute value must be non-negative because it
represents a distance.

13. Class Work 2.2
 Due Tuesday, November 10th
 Do only the odd or even as described
 When solving the equations, be sure to solve for
both the positive and negative values.
 As always, show all the work you did to arrive at
your answers.