Tues, 2/14

SWBAT… solve compound inequalities Happy Valentine’s Day!Agenda

1. WU (10 min)

2. Review compound inequalities HW#3 and HW#4 (20 min)

3. Graphing inequalities: 10 examples - (15 min)

Warm-Up:

HW#5: Graphing Inequalities

HW#2 Answers1. b ≥ -2

2. a < 3

3. m ≤ -40

4. w > 56

5. a ≥ 1

6. h < -15

7. b ≤ -1

8. No Solution

9. All Real Numbers

10. a < 2

11. x > 7

12. s > 37,000

13. t < 4

14. Ana is correct, Laura flipped the sign.

15. The first one does not belong (y > -3 instead of y > 3.)

HW#3 Answers1. f < 11 and f ≥ 6

2. n ≤ -7 and n ≥ -12

3. y ≥ 8 or y < -4

4. t ≥ 1 or t < 19

5. -4 < p ≤ 5

6. -1 ≤ c < 2

7. h ≥ 2 and h < 3

8. m ≤ 6 or m ≥ 6 – Infinite Solutions (All real numbers)

9. a ≤ -4 and a > 4 – No Solution (Empty Set)

10. a ≤ ½ and a > 3 – No Solution (Empty Set)

11. n > -4 and n ≤ 3

12. n < 7 or n ≥ 11

13. n ≤ -4 or n > 1

14. n ≥ 0 and n < 3

Chemistry The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8. The first two readings for the swimming pool are 7.4 and 7.9. What possible values for the third reading p will make the average pH normal?

The value for the third reading must be between 6.3 and 8.1, inclusive.

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

Set up your Cornell Notes… Topic is “Absolute Value Inequalities”

HW#5-Absolute Value Inequalities Answers

1. -24 < x < 8

2. -3 ≤ r ≤ 1

3. -3 ≤ c ≤ 4

4. -3 < h < 5

5. No Solution, Ø

6. All Real Numbers

7. r < -8 or r > 4

8. k < 1 or k > 7

9. p ≥ 22 or p ≤ -14

10. │p – 7.5│ ≤ 0.3

Thurs, 2/16

SWBAT… graph linear inequalities with two variablesAgenda1. Review HW#5 (15 min)

2. Graphing inequalities: 3 examples - (15 min)

3. Due at the end of the period: back of this weeks agenda (15 min)

HW#5: Graphing Inequalities

Set up your Cornell Notes… Topic is “Graphing Linear Inequalities

with two variables”

Graph -y – x < 2Graph -y – x < 2

Step 2: Graph the Step 2: Graph the equality y > -x – 2 equality y > -x – 2

Step 3: Because y > -x – Step 3: Because y > -x – 2 and 2 and notnot ≥, the line ≥, the line will be will be dotteddotted

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0Step 4: Now shade the Step 4: Now shade the side of the line where side of the line where y > -x - 2 (y > -x - 2 (aboveabove the the line).line).

Step 1: Solve the inequality for y: Step 1: Solve the inequality for y: y > -x – y > -x – 22

Graphing a Linear InequalityStep 1) Solve the inequality for y (or for x if there is no y).

Caution: You might need to flip the inequality sign if you multiply or divide by a negative #

Step 2) Graph like before (begin with the b, move the m)

Step 3) If the inequality is < or > (not equals), the line is

dashed (- - - - - - ). If the inequality is ≤ or ≥, the line is solid (______).Step 4) If the inequality is < or ≤, you shade below or to the

left of the line.

If the inequality is > or ≥, you shade above or to the right of the line.

Step 1: Solve the inequality for y: Step 1: Solve the inequality for y: y y ≤ ≤ 2x+1 2x+1 Step 2: Graph the line y ≤ 2x + Step 2: Graph the line y ≤ 2x + 11Step 3: Because y ≤ Step 3: Because y ≤ 2x+1 and 2x+1 and not <,not <, the line the line will be will be solidsolid

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 4: Now shade the Step 4: Now shade the side of the line where side of the line where y < 2x+1 (y < 2x+1 (belowbelow the the line).line).

Graph: y – 2xGraph: y – 2x ≤≤ 1 1

Graph: 3 – x > 0 Step 1: Solve the inequality for x

3 - x > 0

-x > -3

x < 3Step 2: Graph the line x = 3Step 3: Because x < 3, the line will be dottedStep 4: Now shade the side of the line where x < 3 (to the left of the line)

6

4

2

3

Fri, 2/17SWBAT… graph a system of linear inequalities

Agenda

1. WU (10 min)

2. Finish HW#7 (10 min)

3. Graphing systems of linear inequalities: 1 example - (15 min)

3. Finish HW#8

Warm-Up:

1. Re-do correctly the problems that are circled on the back of this week’s agenda.

2.

HW#9: Absolute Value & Inequalities Study Guide

HW#61. y < 2/3x – 2

2. x < 2

3. y > x + 2

y < -x + 1

4. y ≥ –x + 2

y ≥ 2

5. y > x

y > -1/2x + 2

6. y ≥ 2x – 6

y ≥ -3/2x + 6

1.) Given the inequality graphed below:a.) Write an inequality statement.b.) Name one ordered pair that is not in the solution set.c.) Name one ordered pair that is in the solution set.

2. Given the inequality graphed below:a.) Write an inequality statement.b.) Name one ordered pair that is not in the solution set.c.) Name one ordered pair that is in the solution set.

3.) Write a system of inequalities for the dark blue solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

4.) Write a system of inequalities for the green solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

5.) Write a system of inequalities for the dark blue solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

6.) Write a system of inequalities for the dark blue solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

7.) Write a system of inequalities for the blue solution shown on the graph below.

(Hint: you should write 3 different inequalities – one for each graph)

SWBAT… graph systems of inequalities Tues, 2/21Agenda

1. WU (10 min)

2. Review for Thursday’s test (35 min)

WU: Complete on graph paper (collected)1. Graph the inequality 6x – 3y ≥ 12.2. Solve the following system of inequalities by graphing:

-2x + y < -3

-3y + 6 ≤ 2x

Prepare for Thursday’s test

Graphing Systems of Inequalities

Choose a test point to determine which side of the line needs to be shaded.

  The test point for this problem was (0,0).  Always pick a point that is easy to work with.

0 < 2(0) – 3  False0 ≥ (-2/3)0 + 2 False

Since both equations were false, shading occurred on the other side of the line, not

covering the test point.

The solution, S, is where the two shadings overlap one another.

Solution:Let x = the number of weekend adsLet y = the number of weekday ads x + y < 20  (there will be at most 20 ads)200x + 50y < 2200  (the cost of the ads at most $2200)

Review for Thursday’s Test

You will be assigned a problem and you will have to show and explain to the class how you solved it (using the ELMO)

You will then create a similar problem that the class will have to solve (have the answer ready)