1. Do Now 1. Solve 2x+3>x+5 2. Solve - c - 11>23
3. Solve 3(-r-2)<2r+3
X > 2
C < - 34

2. Getting Started
You are riding an elevator and decide you want to see how far it travels in 10 minutes. The table below shows the floors it travels to over time. How far in feet did the elevator travel? (assume 10’ between floors)
Trip 1 2 3 4 5
Floors +8 -6 +9 -3 +7

3. Chapter 1.6 Absolute Value Equations and Inequalities
Target: I can
Write and solve equations and inequalities involving absolute value

4. Solving Absolute Value Equations
Absolute value is denoted by the bars |3|.
Absolute value represents the distance a number is from 0. Thus, it is always positive.
|8| = 8 and |-8| = 8

5. Solving absolute value equations
First, isolate the absolute value expression.
Second, Set up two equations to solve.
For the first equation, drop the absolute value bars and solve the equation.
For the second equation, drop the bars, negate the opposite side, and solve the equation.
Third, solve both equations
Always check the solutions.

6. 6|5x + 2| = 312 6|5x + 2| = 312 |5x + 2| = 52 5x + 2 = 52 5x + 2 = -52
Isolate the absolute value expression by dividing by 6.
6|5x + 2| = 312
|5x + 2| = 52
Set up two equations to solve.
5x + 2 = 52 5x + 2 = -52
5x = x = -54
x = 10 or x = -10.8
Check: 6|5x + 2| = |5x + 2| = 312
6|5(10)+2| = |5(-10.8)+ 2| = 312
6|52| = |-52| = 312
312 = = 312

7. 3|x + 2| -7 = 14 3|x + 2| -7 = 14 3|x + 2| = 21 |x + 2| = 7
Isolate the absolute value expression by adding 7 and dividing by 3.
3|x + 2| -7 = 14
3|x + 2| = 21
|x + 2| = 7
Set up two equations to solve.
x + 2 = x + 2 = -7
x = or x = -9
Check: 3|x + 2| - 7 = |x + 2| -7 = 14
3|5 + 2| - 7 = |-9+ 2| -7 = |7| - 7 = |-7| -7 = 14
= = 14
14 = = 14

8. 2x+5 = -3x – 4 x = 1 |2x+5| = 3x+4 |2x + 5| = 3x +4
Isolate the absolute value expression by adding 7 and dividing by 3.
|2x + 5| = 3x +4
Set up two equations to solve.
2x + 5 = -(3x + 4)
2x+5 = -3x – 4
5x = -9
x = 9/5
Check: |2x + 5| = 3x + 4
|2(-9/5) + 5| = 3(-9/5) /5 = -7/ /5 = -7/5 therefore -7/5 isn’t an answer
2x + 5 = 3x + 4
x = 1
Check: |2x + 5| = 3x + 4
|2(1) + 5| = 3(1) = Therefore 1 is an answer
-2x x

9. Solve
-|3-6x| = 15
No Solution…..How did I know this so fast?

10. Assignment
P. 46 #10-21

11. Day 2
Absolute Value Inequalities

12. Solving Absolute Value Inequalities
Solving absolute value inequalities is a combination of solving absolute value equations and inequalities.
Rewrite the absolute value inequality.
For the first equation, all you have to do is drop the absolute value bars.
For the second equation, you have to negate the right side of the inequality and reverse the inequality sign.

13. Solve: |2x + 4| > 12 2x + 4 > 12 or 2x + 4 < -124 -8

14. Solve: 2|4 - x| < 10 |4 - x| < 5 -1 < x < 9
4 - x < and x > -5
- x < x > -9
x > and x < 9
-1 < x < 9 9 -1

15. Homework
Assignment – p odds and odds and #81 Challenge – #82