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

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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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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

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-8

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1

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-1 x

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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

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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

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-1

1

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y

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x

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Ch 6 Notes Alg 1H 15

p. 343 #5-6

Use a system to solve: 2 variables and 2 inequalities.

Name 3 possible solutions: