Post on 17-Jan-2016
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