New unit on Absolute Value Inequalities 4 weeks

New unit on Absolute Value & Inequalities (4 weeks) Daily HW, WU, exit slips, weekly quizzes SWBAT… 1. Solve absolute value equations. 2. Graph absolute value functions. 3. Solve and graph one-step inequalities involving addition, subtraction, multiplication, and division. 4. Solve and graph multi-step inequalities. 5. Write inequalities in interval notation. 6. Solve and graph compound inequalities. 7. Solve and graph inequalities on the coordinate plane with two variables. 8. Graph a system of inequalities on the coordinate plane with two variables. Unit test on March 22 (before Spring Break)

Wed, 2/1 SWBAT… solve inequalities using addition, subtraction, multiplication, division Agenda 1. WU (5 min) 2. Review HW#1 (10 min) 3. Inequalities charts (10 min) 4. Solving inequalities – 8 examples (20 min) Warm-Up: 1. Take out HW#1 2. Set up notes: Topic = Solving inequalities HW#2: Solving Inequalities

Solving Absolute Value Equations

1 block You walk directly east from your house one block. How far from your house are you? You walk directly west from your house one block. How far from your house are you? It didn't matter which direction you walked, you were still 1 block from your house. This is like absolute value. It is the distance from zero. It doesn't matter whether we are in the positive direction or the negative direction, we just care about how far away we are. 4 units away from 0 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Using Absolute Value in Real Life The graph shows the position of a diver relative to sea level. Use absolute value to find the diver’s distance from the surface.

Definition of Absolute Value The distance from any number to zero on the number line. n The value is always positive. Why? n ¨ Because absolute value is a distance and distance is always positive.

Ex. #1 |x| = 4 x = 4 or x = -4 To solve an absolute value equation: 1. Isolate the absolute value on one side of the equal sign. 2. Case 1: Set the expression inside the absolute value symbol equal to a positive of the other given expression. Solve. 3. Case 2 : Set the expression inside the absolute value symbol equal to the negative of the other given expression. Solve. 4. Check both solutions. Check: |x | = 4 or |x| = 4 | 4 | = 4 | -4 | = 4 4 = 4

Ex. #2 Solve and check: 1. |x + 3| = 7 To solve an absolute value equation: Isolate the absolute value on one side of the equal sign. 2. Case 1: Set the inside of the absolute value equal to a positive of the other given expression. Solve. 3. Case 2 : Set the inside the absolute value equal to the negative of the other given expression. Solve. 4. Check both solutions. x + 3 = 7 or x + 3 = -7 x = 4 or x = -10 Subtract 3 from both sides Check: |x + 3| = 7 or |x + 3| = 7 | 4 + 3| = 7 | -10 + 3| = 7 |7| = 7 |-7| = 7 7 = 7

To solve an absolute value equation: Ex. #3 |15 – 3 x| = 6 15 – 3 x 1. Isolate the absolute value. 2. Case 1: Set the inside of the absolute value (drop the bars) equal to a positive of the other given expression. Solve. 3. Case 2 : Set the inside the absolute value (drop the bars) equal to the negative of the other given expression. Solve. 4. Check both solutions. = 6 or 15 – 3 x = -6 -3 x = -9 -3 x = -21 Subtract 15 from both sides. x=3 or x=7 Divide both sides by – 3. Check: |15 – 3 x| = 6 |15 – 3(3)| = 6 |15 – 3(7)| = 6 |6| = 6 |– 6| = 6 6 = 6

To solve an absolute value equation: Ex. #4 1. Isolate the absolute value. 2. Case 1: Set the inside of the absolute value (drop the bars) equal to a positive of the other given expression. Solve. 3. Case 2 : Set the inside the absolute value (drop the bars) equal to the negative of the other given expression. Solve. 4. Check both solutions. | x | – 6 = -3 | x | = 3 x =3 Add 6 to both sides or x = -3 Check: |x | - 6 = -3 or |x| - 6 = -3 | 3 | = 3 | -3 | = 3 3 = 3

To solve an absolute value equation: Ex. #5 1. Isolate the absolute value. 2. Case 1: Set the inside of the absolute value (drop the bars) equal to a positive of the other given expression. Solve. 3. Case 2 : Set the inside the absolute value (drop the bars) equal to the negative of the other given expression. Solve. 4. Check both solutions. │-3 c│ – 10 = -4 │-3 c│ = 6 Add 10 to both sides -3 c = 6 or -3 c = -6 Divide both sides by -3 c = -2 or c = 2

To solve an absolute value equation: Ex. #6 1. Isolate the absolute value. 2. Case 1: Set the inside of the absolute value (drop the bars) equal to a positive of the other given expression. Solve. 3. Case 2 : Set the inside the absolute value (drop the bars) equal to the negative of the other given expression. Solve. 4. Check both solutions. 2| x | = -10 | x | = -5 No Solution

Absolute Value and No Solutions Absolute value is always positive (or zero). An equation such as │x │= -5 or │x – 4│= -6 is never true. n It has NO solution. n n │x │= -5 has no solution This is a distance And this is negative Ever heard of a negative distance? ? ?

Exit Slip Complete on a separate sheet of paper Solve and check: 1. ) │2 x + 4│ = -12 2. ) │3 c│- 45 = -18