Warm–up #21. Graph x < –3 or 2 < x 5

2. Name the property of inequality that justifies: If 3x + 8 < 7, then 3x < –1

3. Evaluate –

4. Express without absolute value symbols

if x > 1

Warm–up #2 Solutions1. x < –3 or 2 < x 5

2. If 3x + 8 < 7 – 8 – 83x < – 1

Addition Property of Inequality (Add –8)

–3 2 5

Warm–up #2 Solutions3. Evaluate –

= 9 – 12 = – 3

Express without absolute value

symbols4. if x > 1

–1 –1x – 1 > 0

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

= x – 1

Homework LogFri

9/4

Lesson 1 – 2

Learning Objective: To understand properties of absolute value

Hw: #103 Pg. 20 # 57 – 67 odd, 81 – 96 all & extra problems

9/4/15 Lesson 1 – 2 Ordering & Absolute Value Day 2

Advanced Math/Trig

Learning Objective

To understand properties of absolute values

Express without absolute value

symbols1. if x < 4

–4 –4x – 4 < 03(x – 4) < 0 (3)3x – 12 < 0

= – (3x – 12) = – 3x + 12

Express without absolute value

symbols2. if a >

a – > 02(a – ) > 0(2)2a – b > 0

= 2a – b

Less Th”AND”x < 5 AND x > – 5

–5 < x < 5

Great”OR”

x > 5 OR x < – 5

Flip Inequality & Change Sign!

NOT – 5 > x > 5NOT –5 < x > 5

3. Less ThAND

2x – 1 < 5 and 2x – 1 > – 5 +1 +1 +1 +12x < 6 2x > – 4 2 2 2 2x < 3 and x > – 2 – 2 < x < 3

Solve Absolute Value Inequalities

4. Less ThAND– 8 3x – 4 8

+4 +4 +4 –4 3x 12

3 3 3x 4 and x x 4

Solve Absolute Value Inequalities

4. Less ThAND

3x – 4 8 and 3x – 4 – 8 +4 +4 +4 +43x 12 3x –4 3 3 3 3x 4 and x x 4

Solve Absolute Value Inequalities

5. GreatOR

2x + 4 6 or 2x + 4 6 – 4 – 4 – 4 – 42x 2 2x – 10 2 2 2 2

x 1 or x – 5

Solve Absolute Value Inequalities

6. GreatOR

5x + 10 > 25 or 5x + 10 < – 25 – 10 – 10 – 10 – 105x > 15 5x < – 35 5 5 5 5

x > 3 or x < – 7

Solve Absolute Value Inequalities

7. – 4

All Real Numbers

Absolute Value is always positive & will ALWAYS be greater than a negative number!!

Solve Absolute Value Inequalities

8.

No Solution

Absolute Value is always positive & will NEVER be less than a negative number!!

Solve Absolute Value Inequalities

9.

* Know it’s Great“or” >

* Find average of endpoints

*Find how far endpts are from avg: 6

Write an absolute value inequality

10.

* Know it’s LessAnd or Equal to

* Find average of endpoints

*Find how far endpts are from avg: 10

10

Write an absolute value inequality

11.

* Know it’s Great“or” or equal to

* Find average of endpoints

*Find how far endpts are from avg: 8

Write an absolute value inequality

12.

* Know it’s LessAnd

* Find average of endpoints

*Find how far endpts are from avg: 3

Write an absolute value inequality

Homework#103 Pg. 20 # 57 – 67 odd, 81 – 96 all &

Write the absolute value equation for:

1)

2)

& Graph:

3) –5 ≤ 2x+3 < 7

4) x + 3 > 4 OR x + 4 ≤ –1

–4 2

–1 9

1, 2, 3… Natural (N)

0, 1, 2, 3… Whole (W)

… –3, –2, –1, 0, 1, 2, 3…Integers (Z)

Real Numbers (R)Irra

tional (H

)…-, 0.222, 1, 2,

Rational (Q)