Post on 03-Oct-2020
Ch 6 Notes Alg 1H 1
Chapter 6 Notes Alg 1H
6-A1 (Lesson 6-1&2) “Solving Inequalities” p. 301-304
1A) 3
848
n B) 2
423
x Check:
2A) 86
n B)
410
3p
When you multiply or divide by a _________________ number, you must
__________________ the inequality sign!
3A) 9 27r B) 5 40 g C) 32 8 k D) 3 15t
Points:
Ch 6 Notes Alg 1H 2
6-A2 (Lesson 6-3) “Solving Multi-Step Inequalities” p. 308-310
1)
2A) 23 10 2w B) 43 4 11y
3)
4A) 6 5 3 36z z B) 2 6 3 8h h
If solving an inequality results in a __________ statement, the solution is
___________________________.
If solving an inequality results in a __________ statement, the solution is
___________________________.
5A) 18 3 8 4 6 4 1c c B) 46 8 4 2 5m m
Ch 6 Notes Alg 1H 3
6-A3 (Lesson 6-4A) “Solving Compound Inequalities Involving ‘And’ ”
p. 315-316
compound inequality: 2 inequalities ____________________ by the word ________
or the word ________.
“And” type: graph is the _____________________ of the graphs of the 2
inequalities; can be found by graphing each and determining where they
______________
1A) 5 and 0a a B) 6 and 2p p
(Rewrite each of the compound inequalities with the variable between the symbols.)
Check your Understanding p. 317 #1-3
1) 6 and 2a a 2) 12 and 9y y
3) 6 3 and 3 11w w
p. 318 #32) 2 2 4 8 3 3 p p p
Ch 6 Notes Alg 1H 4
6-A4 (Lesson 6-4B) “Solving Compound Inequalities Involving ‘Or’ ”
p. 316-317
“Or” type:
graph is the _________________ of the graphs of the 2 inequalities
its solution is a solution of ____________ inequality
can be found by ________________ each
4A) 1 4 or 1 3a a B) x 9 or 2 4 10x
(If necessary, rewrite each of the compound inequalities in numerical order.)
Check your Understanding p. 317 #4-7
4) 7 5 or -7 1n n
5) 3 1 13 or 1z z
6) 8 4 3x
7)
Ch 6 Notes Alg 1H 5
6-A5 (Lesson 6.2 Heath) “Word Problems with Linear Inequalities”
Heath p. 298-300
Textbook Ex. 2:
“rate of change” is the same as ________________
________________________________ needed to get slope
Whole milk:
Low-fat Milk:
The consumption of low-fat milk ____________________ that of whole milk from
___________________________.
Textbook Ex. 3:
_______________ – __________________________ = __________________
_______________ – (_________________________) = __________________
Ch 6 Notes Alg 1H 6
6-A8 (Lesson 6-5A) “Solving Absolute Value Equations” p. 322-323
Absolute-value: distance from __________
Symbol:
Absolute-value equation: the _______________ is within the absolute
value bars:
Solving an absolute-value equation:
o For c ≥ 0, x is a solution of ax b c if x is a solution of:
_______________ or ________________
o For c < 0, the absolute-value equation ax b c has ____
________________, since absolute value always indicates a number that is
not _________________.
1A) 2 4y B) 3 4 1n
Do p. 325 #1-3
1) 3 10 r 2) 2 8 6 x 3) 4 1 6 n
Ch 6 Notes Alg 1H 7
Always Isolate the Absolute Value term first!!!!!!
Ex. C) 1 2 4 x D) 2 2 8 3 5 x
Check: Check:
p. 323 Ex. 2
Write an open sentence (absolute value equation) from a graph:
Find the _________________
Find the _________________ from the midpoint to the ends.
Equation is: midpoint distancex or ideal variance x
2A) B) (extra example
Do p. 325 #4
HEATH p. 225 (See ex. 5 in textbook)
“Communicating about Algebra”
A. 160 1x B. 189 86x C. 30 10x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
Ch 6 Notes Alg 1H 8
6-A9 (Lesson 6-5B) “Graphing Absolute Value Functions” p. 324
1. Find the ___________________ of the vertex. Ask, “What makes the expression
within the (absolute value bars) equal _________?”
Ex: 4f x x 2 3 4 f x x 3 5 f x x
2. Make a _________________________.
Put the x-coordinate of the __________________ in the center.
Choose some values of x to the __________ and _____________.
3. Complete the y-values.
4. Plot the points. It will make a ________________ graph.
A) 3f x x
Domain:
Range:
x
y
x
y
-1 x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
2
3
4
5
6
7
8
9
10
y
Ch 6 Notes Alg 1H 9
B) 2 1 f x x
Domain:
Range:
C) 2 3 7f x x
Domain:
Range:
Minimum and Maximum Values:
x
y
x
y
-1 x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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9
10
y
-1 x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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7
8
9
10
y
Ch 6 Notes Alg 1H 10
6-A10 (Lesson 6-6A) “Solving Absolute-Value Inequalities” p. 329-331
Types of absolute-value inequalities:
o “And” type: ___________; graph is ________________2 values
o “Or” type: ___________; graph is ________________2 values
to solve: use the __________________ and ___________________ case
of the expression inside the ______________________ and solve it twice.
1A) 8 2n 2A) 2 1 7k B) 2 4 1 x
p. 331 CYU #1,2,4,5, Extra Ex.
1) 2 6 c 2) 5 3 x 4) 10 15 w
5) 2 5 7 g Extra Ex.)
2 3 2 1 7 x
Ch 6 Notes Alg 1H 11
6-A11 (Lesson 6-6B) “Types of Absolute-Value Inequalities”p. 329-331
Concept Summary:
If , then or .
If , then .
If , then or .
x n x n x n
x n n x n
x n x n x n
If , then there is _____________________.
If , then the solution is ______________________.
x n
x n
1B) 2 5 3x 2B) 6 5r p. 331 #3,6,7
Heath “Communicating about Algebra” p. 315
ax b c ax b c
b: ______________________________________
c: ______________________________________
A) B)
In the above examples, we transformed a _______________________ inequality into an
______________________ inequality.
-3 5 –3 -1
Ch 6 Notes Alg 1H 12
6-A15 (Lesson 6-7) “Graphing Linear Inequalities in Two Variables” p. 334-337
Linear inequality: can be written as:
________________
________________
________________
________________
Graphing a linear inequality:
Graph _____________________________.
Use a _____________________ for > or <.
Use a _____________________ for ≤ or ≥.
Test an ____________________________ in one of the half-planes.
Shade the _____________________ containing the solution.
1A) 1x B)
13
2y x
C) 4y D) 2 3y x
-1 x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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9
10
y
-1 x
-10
-9
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-7
-6
-5
-4
-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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10
y
-1 x
-10
-9
-8
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-6
-5
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-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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y
-1 x
-10
-9
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-7
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-5
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-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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y
Ch 6 Notes Alg 1H 13
E) 4 2 2x y F) 1 y x
p. 337 #7
Will the coach be able to buy 4 pizzas and 6 pitchers of drinks?
-1 x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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y
-1 x
-10
-9
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-10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 -1
1
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y
Ch 6 Notes Alg 1H 14
6-A16 (Lesson 6-8) “Graphing Systems of Inequalities” p. 341-342
System of inequalities: ___________ inequalities with the same
_________________; solved together
Solution of a system: a region of a ____________ that shows the
___________________ or _______________ of the graphs of the
inequalities.
1A) 3 1y x y B) 2 2 2 7x y x y
C) 3 4y y x D) 4 2 6 2 1x y y x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
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10
y
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
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y
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
x
-10
-9
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-7
-6
-5
-4
-3
-2
-1
1
2
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y
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
x
-10
-9
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-3
-2
-1
1
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y
Ch 6 Notes Alg 1H 15
p. 343 #5-6
Use a system to solve: 2 variables and 2 inequalities.
Name 3 possible solutions: