Download PRE-AP Algebra 3 Ch.2S7 Absolute Value - cguhs

Bell work
1. Solve and graph the compound inequalities.
Write your solutions in set and interval notation.
a. 4 > - x + 3 > - 6
b. -2x + 4 <
-3
or
x+5<3
Bell work answers
1.
a. 4 > - x + 3 > - 6
-3
-3
-3
1 < -1x<-9
-1
-1
-1
{x | -1 < x < 9} = [- 1, ∞ ) Ո (- ∞ , 9) = [-1, 9)
--|-----|-----|-----|-----|-----|----|-----|------|-----|-----|-----|-----|-----|
-2 -1
0
1
2
3 4
5
6
7
8
9
10 11
Bell work answers
1. b. -2x + 4 < - 3
-4
-4
-2x < -7
-2
-2
or
or
x+5<3
-5 -5
x < -2
{x | x > 7/2 or x < -2} = (- ∞, -2 ) Ս [7/2 , ∞ )
--|-----|-----|-----|-----|-----|----|-----|------|-----|-----|-----|-----|-----|
-6 -5
-4 -3 -2 -1 0
1
2
3
4
5
6
7
Pre-AP Algebra 3
Chapter 2 Section 7
Objective: Students will:
1. Simplify expressions with absolute
value.
2. Find the distance between two
points on a number line.
3. Solve equations and inequalities
with Absolute value by converting to
compound statements.
Absolute Value
Definition:
For all real numbers x,
|x| = X if x is non negative
|x| = - x if x is negative
opposite
Properties of Absolute Value
A. For all real numbers a, and b.
|ab| = |a|•|b|
B. |a/b| = |a|/|b|
n
n
C. |a | = a if n is an even integer
Simplifying Expressions
Examples:
a. |7x|
= 7|x|
d. | (7a)/ b²|
= 7|a|/b²
b. | x⁸|
= x⁸
c. |5a²b|
= 5a²|b|
e. |-9x|
= 9|x|
Distance on the number line
Definition: the distance between any two points on
a number line having coordinates “a” and “b”
is |a – b| or |b – a|
Example: Find the distance between -3 and 2.
-----|-----|-----|-----|-----|-----|-----|-----
- 4 -3 -2 -1
0
1
2
= | -3 -2| = | -5| = 5 or |2 – (- 3)| = |5| =5
The distance between -3 and 2 is 5 units.
Distance between two numbers
Example 2: Find the distance between - 23 and -17
| -23 – (-17)| = |-23 + 17| = |-6| = 6
or
| - 17 – (-23)| = |-17 + 23| = |6| = 6
Principles for Solving
Equations/Inequalities with
Absolute Value (p. 90)
For any positive number “b” and any
expression |N|
To solve:
A. |N| = b satisfies N =- b or N = b
B.|N| < b satisfies - b < N < b
C. |N| > b satisfies N< -b or N > b
Solving Equations/Inequalities with
Absolute Value
Example 1: Solve |3x + 4| = 9
To solve | 3x +4 | = 9 write and solve a
compound statement:
3x + 4 = - 9
or
3x + 4 = 9
-4
-4
-4 -4
3x = -13
or
3x = 5
3
3
3
3
Solution x = -13/3 or x = 5/3
Graph: --|-----|-----|-----|-----|-----|-----|-----|--
-5 - 4 -3 -2 -1
0
1
2
Solving Equations/Inequalities with
Absolute Value
Example 2: Solve |2x – 3| < 7
To solve |2x – 3| < 7 write a compound statement
-7 < 2x – 3 < 7
+3
+3 +3
- 4 < 2x < 10
2
2
2
Solution: -2 < x < 5
Graph: --|-----|-----|-----|-----|-----|-----|-----|--
-2 -1
0
1
2
3
4
5
Solving Equations/Inequalities with
Absolute Value
Example 2: Solve |2x – 4| > 7
To solve |2x – 4| > 7 write a compound statement
2x – 4 < - 7
or
2x – 4 > 7
+4
+4
+4 +4
2x < - 3
or
2x > 11
2
2
2
2
Solution: x < - (3/2) or
x > (11/2)
Graph: --|-----|-----|-----|-----|-----|-----|-----|--
-2 -1
0
1
2
3
4
5
Homework
PRE _AP ALGEBRA 3
P. 91 (2 - 50) even
Journal Topic
Write about what you learned from today’s
lesson.