Chapter 6 Class NotesAlg. 1CP

6-1 “Solving Inequalities Using Addition and Subtraction” p. 297

1. 2. 3. 4.

6-2 “Solving Inequalities Using Multiplication and Division”p. 301-304

1A) B) 2A) B)

When you multiply or divide by a ______number, you must ______the inequality sign!

3A) B) C) D)

Points:

6-3 “Solving Multi-Step Inequalities”p. 308-310

1)

2A) B)

3)

4A) B)

If solving an inequality results in a ______statement, the solution is ______.

If solving an inequality results in a ______statement, the solution is ______.

5A) B)

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Ch. 6 Notes 8CP

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) B)

(Rewrite each of the compound inequalitieswith the variable between the symbols.)

Check your Understanding p. 317 #1-3

1) 2)

3)

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Ch. 6 Notes 8CP

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

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Ch. 6 Notes 8CP

4A) B)

(If necessary, rewrite each of the compound inequalities in numerical order.)

Check your Understanding p. 317 #4-7

4)

5)

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Ch. 6 Notes 8CP

6)

7)

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Ch. 6 Notes 8CP

6-5A “Solving Absolute Value Equations”p. 322-323

Absolute-value: distance from ______

Symbol:

Absolute-value equation: the ______is within the absolute value bars; form:

Solving an absolute-value equation:

  • For c ≥ 0, x is a solution of if x is a solution of:

______or ______

  • For c < 0, the absolute-value equation has ______, since absolute value always indicates a number that is not ______.

1A) B)

Do p. 325 #1-3

1) 2) 3)


Always Isolate the Absolute Value term first!!!!!!

Ex. C) D)

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:

2A) B) (extra example)

1

1

1

Do p. 325 #4

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:

  1. Make a ______.
  2. Put the x-coordinate of the ______in the center.

x
y
  • Choose some values of x to the ______and ______.
  1. Complete the y-values.
  2. Plot the points. It will make a ______graph.

A)

x
y

Domain:

Range:

B)

x
y

Domain:

Range:

C)

x
y

Domain:

Range:

Minimum and Maximum Values:

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6-7 “Graphing Linear Inequalities in Two Variables”p. 334-337

Linear inequality: can be written as:

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  • ______
  • ______
  • ______
  • ______

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Graphing a linear inequality:

  • Graph ______.

Use a ______for > or <.

Use a ______for ≤ or ≥.

  • Testan ______in one of the half-planes.
  • Shade the ______containing the solution.

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1A)

B)

C)

1

1

D) E) F)

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Study Guide for Absolute ValueChapter 6Alg. 1CP

Type of Problem / How to Solve
/ Write ____ equations; ______
/ No solution; can’t have a ______answer unless there is a neg. sign in front of the
/ Write 2 equations and ______; ______
/ ______the ab. value term (subtract 2); Then write 2 equations and solve; ______
/ Write as an ______type of compound inequality.
______
/ Write as an ______type of compound inequality.
______
/ Write as an ______type of compound inequality.
______Then ______.
/ ______the ab. value term (divide by 2); Then write as an ______type of compound inequality.
Then ______.

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) B)

C) D)

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