Wed, 2/1

SWBAT… solve inequalities using addition, subtraction, multiplication, divisionAgenda

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#12. Set up notes: Topic = Solving inequalities

HW#2:Solving Inequalities

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)

< > ≤ ≥

Endpoints (when graphing on a number line)

< > ≤ ≥

Open Circle Open Circle Closed circle Closed circle

Interval Notation

< > ≤ ≥

( ) ( ) [ ] [ ]

Examples:

x > 4

(4, ∞ )

-2 ≤ x ≤ 5

[-2, 5]-2 < x ≤ 5 (-2, 5]

0 4

-2 0 5

-2 0 5

Interval Notation

< > ≤ ≥

( ) ( ) [ ] [ ]

Examples:

x ≥ 4 or x < 1

(-∞, 1) [4, ∞)

Always use parenthesis with Infinity

0 1 4

1st, Tues, 2/7

SWBAT… solve inequalities using addition, subtraction, multiplication, divisionAgenda

1. WU (10 min)

2. Review HW#1: Absolute value inequalities (10 min)

3. Solving inequalities – 8 examples (25 min)

Warm-Up:

1. Solve for n: 3.7| n | + 10.6 = 3.22. Solve for x: 7.25| x + 1 | + 6.8 = 21.3

HW#2:Solving Multi-Step Inequalities

Solving and Graphing Inequalities by Addition and Subtraction

Directions: Solve the inequality, graph the solution on a number line.

Ex 1: d – 14 ≥ -19Ex 2: 22 > m – 8Ex 3: Three added to a number is no

more than twice the number.

WARNING!!!!! (Example 2 & 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 < x as

x < 3 The inequality sign always points to the lesser value

(or it’s eating the bigger number.) In 3 < x, the inequality points to 3, so to write the

expression with x on the left, use x > 3

Solving and Graphing Inequalities by Multiplication and Division

Very important….

When you multiply or divide each side of an inequality by a negative number you always reverse or flip the inequality sign.

< >

> <

≤ ≥

≥ ≤

7 > 4 7(-2) > 4(-2)

-14 > -8

NOT TRUE!

You must change the inequality symbol

-14 < -8

RATIONALERATIONALE

Ex 1: -7d ≤ 147 Ex 2: 5n ≤ -25

Ex 3:

Ex 4:

Ex 5:

217

3 r

86

n

36

x

Directions: Solve the inequality, graph the solution on a number line.

Solving and Graphing Multi-Step Inequalities

Tues, 2/7

SWBAT… solve multi-step inequalities

Agenda:

1. Five WU problems below (15 min)

2. Double math courses (5 min)

3. Review HW#2 – multi-step inequalities (10 min)

4. Review Quiz (5 min)

5. Electra’s truck problem (10 min)

WU: Solve each inequality & write in interval notation:

1. 6(x – 11) – 4x ≤ -72

2. Two times the difference of a number and five is no more than eight.

3. -7(k + 4) + 11k ≥ 8k – 2(2k + 1)

4. 2(4r + 3) ≤ 22 + 8(r – 2)

Geometry AND Honors Advanced Algebra with Trigonometry (Algebra II)

Infinity Math Sequence for students that take Geometry and Honors Advanced Algebra in 10th grade:

9th 10th 11th 12th

*Honors or Regular Algebra

*Honors or Regular Geometry and Honors Advanced Algebra

*Honors Pre-Calculus

*AP Statistics

(college credit ≥ 4) (optional)

*AP Calculus (college credit ≥ 4)

*AP Statistics (college credit ≥ 4) (optional)

Electra needs to rent a truck for a day to move some furniture. The table below shows the rates of the two truck-rental companies near her home.

a.) Write an inequality that Electra can use to find the maximum number of miles that she can drive and spend less with Company A than Company B. Be sure to identify your variable or variables.

b) Find the maximum number of miles that Electra can drive so that she spends less than she would for a truck rented from Company B.

Company Daily rate Per mile charge

A $29.95 $0.87

B $72.00 $0.00

Thurs, 2/9

SWBAT… solve compound inequalitiesAgenda

1. WU (5 min)

2. Solving compound inequalities – 6 examples (25 min)

3. Two open ended compound inequalities (10 min)

4. Work on HW2 or HW3 (10 min)

Warm-Up:

1. -(3t – 5) + 7 > 8t + 3

HW#3:Solving Compound Inequalities

Solving and Graphing Compound Inequalities

Inequalities Containing and To ride a roller coaster, you must be at least 52 inches tall, and your height

cannot exceed 72 inches. If h represents the height of the rider, we can write two inequalities to

represent this.

At least 52 inches Cannot exceed 72 inches

h ≥ 52 and h ≤ 72

The inequalities h ≥ 52 and h ≤ 72 can be combined and written without

using “and” as 52 ≤ h ≤ 72 Graph the inequality “sandwich”

Variable is isolated

You try!Solve and graph the compound inequality. Write it two different ways.

1.) -2 < x – 3 < 4

2.) -5 < 3p + 7 ≤ 22

Inequalities Containing and

Inequalities Containing or

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.

Let t = temperature

t < 75 or t > 90

Graph the inequality “torpedo”

You try!

Solve and graph the compound inequality.

1. 5n – 1 < -16 or -3n – 1 < 8

2. The product of -5 and a number is greater than 35 or less than 10.

Inequalities Containing or

OPEN ENDED 1: Write a compound inequality containing and for which the graph is the empty set.

Sample answer: x ≤ -4 and x ≥ 1

OPEN ENDED 2: Create an example of a compound inequality containing or that has infinitely many solutions.

Sample answer: x ≤ 5 or x ≥ 1

Tues, 2/

SWBAT… solve compound inequalities Agenda

1. WU (10 min)

2. Review HW3 and HW#4 (20 min)

Solve the inequality:

1.) Solve for a: 12 – (a + 3) > 4a – (a – 1)

HW4: Solving Compound Inequalities: Chemistry & Geometry

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