Mon, 2/22/10 SWBAT… solve inequalities using addition and subtraction Agenda WU (5 min) Test results (10 min) Solving inequalities – 5 examples (20 min) Work on hw#1 (15 min) Warm-Up: 1. Write hw in planner 2. Take out hw (back of last week’s agenda) 3. Set-up notes. Topic = Solving Inequalities by Addition and Subtraction HW#1:Solving Inequalities by Addition and Subtraction 1

Phrases for Inequalities < > ≤ ≥

Phrases for Inequalities < > ≤ ≥ less than fewer than greater than more than at most, no more than, less than or equal to at least, no less than greater than or equal to

Endpoints (when graphing on a number line) < > ≤ ≥ Circle Dot

Directions: Solve the inequality Directions: Solve the inequality. Then graph the solution on a number line. Example 1: x – 12 ≥ 8 Example 2: d – 14 ≥ -19 Example 3: 22 > m – 8 (next slide) Example 4: 3a + 6 ≤ 4a Example 5: 9n – 1 < 10n Example 6: Three more than a number is less than twice the number. 1.) x ≥ 20 2.) d ≥ -5 3.) m < 30 4.) a ≥ 6 5.) n > -1 6.) Let n = a number 3 + n < 2n (subtract n from both sides) 3 < n n > 3

WARNING!!!!! (Example 3) An equation such as x = 5 can be written as 5 = x (because of the Symmetric Property of Equality) You CANNOT rewrite an inequality such as 3 > y as y > 3. The inequality sign always points to the lesser value. In 3 > y, it points to y, so to write the expression with y on the left, use y < 3.

A more concise way of writing a solution set is to use set-builder notation. {x │x ≥ 20} is read the set of all numbers x such that x is greater than or equal to 20.

HW#2:Solving Inequalities by Multiplication and Division Tues, 2/23/10 SWBAT… solve inequalities using multiplication and division Agenda WU (10 min) Solving inequalities with multiplication and division Warm-Up: Write hw in planner Set-up notes. Topic = Solving Inequalities by Multiplication and Division Review hw#1 HW#2:Solving Inequalities by Multiplication and Division 8

Topic is “Solving Inequalities by Multiplication and Division”

One eighth times the number of students surveyed is less than 84 Of the students surveyed at LVLHS, fewer than eighty-four said they have never purchased an item online. This is about one eighth of those surveyed. How many students were surveyed? Understand: You know the number of students who have never purchased an item online and the portion this is of the number of students surveyed. Plan: Let n = the number of students surveyed. Write a sentence that represents this situation. One eighth times the number of students surveyed is less than 84 1/8 ∙ n < 84 Solve: Solve for n (8)1/8n < 84 (8) n < 672 Check: To check, substitute a number less than 672 into the original inequality. The solution set is {n│n < 672}. This means that there are fewer than 672 students who were surveyed at LVLHS.

Example 1: Example 2: Example 3: Example 4: -7d ≤ 147 1.) r > -49 2.) n > -48 3.) x > -18 (Do change the inequality sign) 4.) d ≥ -21

Wed, 2/23/10 SWBAT… solve inequalities using multiplication and division Agenda Review hw#2 (10 min) Entry document – project (25 min) Conference call with Michael at 10:50am (10 min) Warm-Up: Write hw in planner Work on project!!!! Presentations are in class Friday! HW#3 (both sides) -due Monday! 12

RATIONALE If you multiply or divide each side of an inequality by a negative number, the inequality symbol changes direction 7 > 4.5 7(-3) > 4.5(-3) -21 > -13.5 NOT TRUE! You must change the inequality symbol -21 < -13.5

s = the number of students in a group 3 ≥ s ≥ 2 How many students can be in a group?

Michael will be here tomorrow to listen to your recommendations! You will be graded on this mini-project based on the rubric (which Michael will complete) PLEASE DON’T EMBARASS ME!!!!!!!!! 

Tues, 3/2/10 SWBAT… solve multi-step inequalities Agenda WU (15 min) Review hw#3 (10 min) Presentations/Ithaca Car Sharing Case (20 min) Warm-Up. Solve each inequality. 4(3t – 5) + 7 > 8t + 3 -7(k + 4) + 11k ≥ 8k – 2(2k + 1) 2(4r + 3) ≤ 22 + 8(r – 2) Two times the difference of a number and five is greater than seven. 1.) t > 4 2.) Empty set 3.) All real numbers 4.) n = number; 2(n – 5 ) > 7; n > 7 HW: Study for Quiz! 16

9th Period: Tues, 3/2/10 SWBAT… solve multi-step inequalities Agenda WU (15 min) Review hw#3 (10 min) 2 examples from exit exam (20 min) Warm-Up. Solve each inequality. 4(3t – 5) + 7 > 8t + 3 -7(k + 4) + 11k ≥ 8k – 2(2k + 1) 2(4r + 3) ≤ 22 + 8(r – 2) Two times the difference of a number and five is greater than seven. 1.) t > 4 2.) Empty set 3.) All real numbers 4.) n = number; 2(n – 5 ) > 7; n > 7 HW: Study for Quiz! 17

Wed, 3/3/10 SWBAT… solve compound inequalities Agenda Quiz (15 min) Correct quiz (5 min) Notes - Solving compound inequalities (30 min) HW#4: Solving Compound Inequalities 18

SPEED The maximum speed limit on an interstate highway is 70 mph and the minimum is 40 mph. Write an inequality that represents this. Sample answer: Let r = rate of speed 40 ≤ r ≥ 70

SNAKES Most snakes live where the temperature ranges from 750 F to 900 F. Write an inequality to represent temperatures where snakes will not thrive. Sample answer: Let t = temperature t < 75 or t > 90

OPEN ENDED: Write a compound inequality containing and for which the graph is the empty set. Sample answer: x ≤ -4 and x ≥ 1 OPEN ENDED: Create an example of a compound inequality containing or that has infinitely many solutions. Sample answer: x ≤ 5 or x ≥ 1

GEOMETRY The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side. a.) Write and solve three inequalities to express the relationships among the measures of the sides of the triangle shown above. b.) What are the possible lengths for the third side of the triangle? c.) Write a compound inequality for the possible values of x. 9 x 4 a.) x + 9 > 4, x > -5 x + 4 > 9, x > 5 4 + 9 > x, x < 13 b.) 6, 8, 9, 10, 11, 12 c.) 5 < x < 13