Warm–up #11. In which set does belong?

2. In which set does belong?

3. Find Z W

4. Find Z W

5. A = {1, 3, 5, 7}, B = {2, 4, 6, 7}

Find A B

Warm–up #1 Solutions1. = 3 N, W, Z, Q, R

2. = 2.828… H, R

3. Z W W

4. Z W Z

5. A = {1, 3, 5, 7}, B = {2, 4, 6, 7}

Find A B {1, 2, 3, 4, 5, 6, 7}

Lesson 1 – 2 Ordering & Absolute Value Day 1

Advanced Math/Trig

Learning Objective

To order real numbers

To graph inequalities

To understand properties of addition & multiplication of inequalities

To understand properties of absolute values

Number Line

0 1 2 3 4 5 6-1-2-3-4-5-6origin

less<

greater>

2 1.41 3.14

2

1. Graph: –1 ≤ x < 3

x ≥ –1 AND x < 3 (AND is the overlap)

–1 3≥ or ≤ closed circle

< or > open circle

Another way:since x is in between –1 & 3,shade in between

2. Graph: x > 2 OR x ≤ 0

0 2

3. Write a statement that has the

given graph

3 8–2

–2 ≤ x ≤ 3 OR x > 8

Properties of Inequality

Addition Property:

If x > 3

then, x + 2 > 3 + 2

Properties of Inequality

Multiplication Properties:

If 2x > 8, then x > 4

Mult by ½

If –2x > 8, then x < –4

Mult by –½

(Flip inequality

sign if mult. or divide by a negative

#)FLIP!!

Name the property of

inequalities that justifies each

statement

1. If 5x > 10, then x > 2

Mult. Prop of Ineq (Mult by 1/5)

2. If 3 + x < 2 + 2x, then 3 < 2 + x

Add Prop of Ineq (Add –x)

3. If x > 0, then 5x > 0

Mult. Prop of Ineq (Mult by 5)

Absolute Value

if 0 if 0a aa a a

7 7 7 7 7 9 2 2 treat like ( )

7 9 7 9 2

Express without absolute value

symbols1. if x > 5

–5 –5x – 5 > 0

Use the definition! So it’s equal to exactly what’s inside the absolute value

= x – 5

Express without absolute value

symbols2. if x < 5

–5 –5x – 5 < 0

Use the definition! So it’s equal to the negative of whatever is inside the absolute value

= – (x – 5) = –x + 5

Express without absolute value

symbols3. if x > 2

–2 –2x – 2 > 0

Use the definition! So it’s equal to exactly what’s inside the absolute value

= x – 2

Express without absolute value

symbols4. if x < 8

–8 –8x – 8 < 0

Use the definition! So it’s equal to the negative of whatever is inside the absolute value

= – (x – 8) = –x + 8

Ticket Out the Door

Express without absolute values if x < 2

Explain how you came up with your answer

Homework

#102 Pg. 18 # 1 – 55 odd