Welcome! Please do the following: 1) Take out Colored Pen. 2) Take out U1H2. 3) Pick up one whiteboard per person.

Transcription

1 Welcome! Please do the following: 1) Take out Colored Pen. 2) Take out U1H2. 3) Pick up one whiteboard per person. Tear Out Pages: Ø Pg. 14, 16 (Put away; this is homework)

2 Welcome! U1H3: Pg. 14 #6-14 AND pg. 16 #23-25 SKIP #10, 23, 25 Updates: U1Q2 will be 9/2 (On September 1 st you will need your Graphing Calculator)

3 Agenda 1 Materials Quiz (Day 3) 2 Warm-Up! 3 Review U1H2 4 U1Q1 5 Absolute Value Equations 6 Absolute Value Inequalities 7 Cool-Down!

4 Materials Quiz Please hold up the colored pen! The rest of the materials quiz will be the graphing calculator (3 points). I will enter the points out of 7 initially, but on Sept. 1 st I will enter it out of 10 points. If you forgot any materials please speak with me after class.

5 Warm-Up! On your whiteboard do the following: Ø Is the following a function? The color of a car to its brand. Ø A line passes through two points (4, 7) and (7, 11). Write the equation of the line in standard form.

6 Warm-Up! Ø A reception hall can hold up to 200 people. The cost of having a luncheon is $12 per person plus $35 charge for preparing the room. Write a function to represent the cost of having a luncheon.

7 U1H2 Grade homework in a colored pen. Ask as many questions to support your success!

8 U1Q1 Ø Put everything away except for a pencil and eraser. Ø No calculators, no pens, if you want to use a highlighter to highlight important information you can. Ø You will be given 15 minutes to complete the quiz. Once the time is up you will not be given any extra time. Ø When you einish bring your quiz up to me and return to your seat. You may work on another classes homework. NO CELLPHONES!

9 Setting up your Notebook Today s Lesson #: 3-1 Topic: Absolute Value Equations and Inequalities LO#3: Solve and graph absolute value equations and inequalities.

10 3-1 Absolute Value Equations and Inequalities Before we begin you need to recall how to solve linear inequalities. On your whiteboard solve each inequality. Ø y + 7 < -11 Ø 4m -12 Ø 5 2x 17

11 x > 3 OR x < -2 This cannot be written 3-1 Absolute Value Equations and Inequalities Sometimes a solution will include two sets of solutions such as: -2 < x or/and x < 3 Compound Inequality o Two inequalities are connected by and or or. o And if the two sets are connected (overlap). o Or if the two sets are disconnected. -2 < x AND x < 3 If I graphed this on a number line I would [ind that they overlap, hence, we can rewrite it as -2 < x < 3

12 3-1 Absolute Value Equations and Inequalities **Reminder** Open Dot Closed Dot * <, > *, =, * Not equal to * Equal to

13 Whiteboards! Rewrite as an AND or OR. Ø x 12 OR x < -16 Ø x > -1 AND x < 3 Ø x 0 OR x > 2 Ø Rewrite x > -1 AND x < 3 as a single inequality.

14 3-1 Absolute Value Equations and Inequalities Practice #1: Solve the compound inequality. Then graph the solution set. (a) 6y < 24 OR y +5 3 (b) ½ c -2 AND 2c + 1 < 1 I printed a slip of paper with all the practice problems that we will glue/tape into our notebooks at the end of the lesson. J

15 3-1 Absolute Value Equations and Inequalities Ø Recall, what is the deeinition of absolute value? (1 min.) Absolute Value o A number x, written as x, is the distance from x to zero on the number line. o The absolute value of any real number is nonnegative.

16 3-1 Absolute Value Equations and Inequalities Practice #2: Solve each absolute value equation. (a) 3 + k = 10 (We will do together) (b) 6x 8 = 22 (c) x = - 2 (d) x = 1

17 3-1 Absolute Value Equations and Inequalities The solutions of x < 3 are the points that are less than 3 units from zero. The solution is an AND: 3 < x < 3.

18 3-1 Absolute Value Equations and Inequalities The solutions of x > 3 are the points that are more than 3 units from zero. The solution is an OR: x < 3 or x > 3.

19 3-1 Absolute Value Equations and Inequalities Note: The symbol can replace <, and the rules still apply. The symbol can replace >, and the rules still apply.

20 3-1 Absolute Value Equations and Inequalities Practice #3: Solve each inequality and graph the solution. (a) 3 + k < 10 (We will do together) (b) 2x > 6 (c) 5x

21 3-1 Absolute Value Equations and Inequalities We have learned how to list items (in braces { }). What if items are intervals such as 3 < x < 7. Can we write this in a form other than as an inequality? YES! Interval Notation!

22 3-1 Absolute Value Equations and Inequalities Interval Notation o A shortcut for writing an inequality solution set. o [ Bracket(s) include endpoints. Represented by closed dots. o ( Parentheses exclude endpoints. Represented by open dots. o Written from least to greatest. In a colored pen, we are going to add interval notation to all solution sets with an inequality.

23 Whiteboards! Rewrite using interval notation. Ø x 12 OR x < -16 Ø x > -1 AND x < 3 Ø x 0 OR x > 2 Tape or Glue the practice problems below your notes J

24 Cool Down We are going to revisit the Unpacked Embedded Assessment. Quickly reread todays learning objective. Which skill/knowledge would satisfy LO#3?

25 Extra Practice