Warm–up #2. Warm–up #2 Solutions –3 2 5 Warm–up #2 Solutions.
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Transcript of Warm–up #2. Warm–up #2 Solutions –3 2 5 Warm–up #2 Solutions.
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)