Equations, Inequalities,

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Chapter 7

• Equations, Inequalities, Functions

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7.1 Daily Puzzler

• If 3! 3 x 2 x 1 and 5! 5 x 4 x 3 x 2 x 1,
  evaluate 10!/8!

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Add to Definition Sheet Lessons 1-3
Verbal model- Inverse operation- Terms- Like
terms- Equivalent variable expressions- Coefficien
t- Constant term- Addition Property of
Equality-adding the same number to each side of
an equation produces an equivalent equation. X
a b x a b a
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In the Real World

• You are exploring a cave in which rock formations
  called stalagmites grow up from the cave floor.
  The tour guide informs you that the tallest
  stalagmite in the cave is in a pool of water 55
  feet deep, and the distance between the tip of
  the stalagmite and the surface of the water is 41
  feet. How tall is the stalagmite?

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Translating Phrases and Sentences

• In real life situations you may need to translate
  verbal phrases (a number increase by 5) into
  variable expressions (m 5) and equations (uses
  equal signs m 5 25).
• C\Documents and Settings\administrator\My
  Documents\Expressions_and_Statements.asf

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Your turn now

• A number added to -7
• 4 decreased by the quotient of a number and 7
• 3 more than twice a number
• The sum of a number and -9 equals 24
• ¼ the difference of 6 and a number is 200
• The sum of -4 times a number and 3 is 27

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7.1 Concept Check

• Write expressions for the difference of b and c
  and the difference of c and b.

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7.2 Daily Puzzler

• Solve the equation SEVEN EIGHT TWELVE by
  finding the correct digit to be substituted for
  each of the 10 different letters in this puzzle,
  using each of the digits 1 through 9.

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Simplifying Expressions

• Parts of an expression can be grouped together by
  like terms.
• Example 2x 3x (2 3)x 5x
• Example 7c 9 3c
• 7c 3c 9
• 4c 9
• Example X 4 2x -10
• X and -2x are like terms, 4 and -10 are like
  terms
• 4 and -10 are constant terms
• 1 and 2 are the coefficients
• http//instantprojects.org/webquest/webquest.php?A
  uthorID4606

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Your Turn Now

• Simplify
• 4d 6 5d
• -3z 4z
• Name the coefficients, constant terms, like
  terms
• 3x 6 x 10
• 15 9r 7r 6

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7.2 Concept Check

• What are like terms?

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7.3 Daily Puzzler

• Using four 4s and some arithmetic operations,
  write expressions equal to 6 and 7.

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Space Exploration

• The Apollo 11 mission lasted about 195.5 hours.
  The flight from Earth to the moon lasted about 10
  hours, and the flight from the moon back to Earth
  lasted about 71 hours. About how many hour did
  the Apollo 11 astronauts spend on the moon?
• Write a verbal model. Let t represent the number
  of hours the astronauts spent on the moon.

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Addition Property of Equality

• Adding the same number to each side of an
  equation produces an equivalent equation.
• X 7 -10
• -7 -7
• X -17

Subtraction Property of Equality
Subtracting the same number from each side of an
equation produces an equivalent equation. -9 y
12 12 12 3 y
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Your turn now

• C 5 8
• -16 5.5 x 3.5
• T 3 2
• 5.7 9 p 1
• 3y 2y 3/5 4/7
• While holding his cat. Bill steps on a scale. The
  result is 127 pounds. Alone, Bill weighs 112
  pounds. Write and solve an equation to find the
  weigh of Bills cat.

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7.3 Concept Check

• Solve x (-3) -4. did you add or subtract from
  both sides? Explain.

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7.4 Daily Puzzler

• Using four 4s and some arithmetic operations,
  write expressions equal to 5 and 9.

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Add to definition Sheet

• Division Property of Equality-Dividing each side
  of an equation by the same nonzero number
  produces an equivalent equation.
• Multiplication Property of Equality-Multiplying
  each side of an equation by the same nonzero
  number produces an equivalent equation.

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Flying Disc

• You throw a flying disc to your dog. It stays in
  the air for 2.5 seconds before you dog catches it
  30 feet away from you. Write and solve a
  multiplication equation to find the speed of the
  disc.

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Solving multiplication Equations

• -3x 45
• -3x 45
• 3 3
• X -15

-6x 84 -6x 84 6 6 X -14
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Solving Division Equations

• m/2 0.75
• 2 x m/2 2 x 0.75
• m 1.5

-4 2/3k (3/2)(-4) (3/2)2/3k -6 k
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Your Turn

• 14q 42
• w/2 8
• 9s -27
• -3/4y 12
• x/6 12
• -3/10z -6
• A blimp travels 300 miles in 7.5 hours. Assuming
  that the blimp travels at a constant speed, write
  solve an equation to find the speed of the
  blimp.

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7.4 Concept Check

• How would you solve 1/5x 15?
• And 5x 15?

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7.5 Daily Puzzler

• Suppose you were building a pyramid of board
  erasers, placing one on the top, two in the
  second row, three in the third row, an son on.
  How many erasers will you need to make a pyramid
  with 20 rows?

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Solving Two-Step Equations

• 5x 6 -21
• 5x 6 6 -21 6
• 5x -15
• 5x -15
• 5 5
• X -3

c/3 13 0 c/3 13 -13 0 -13 c/3 -13 3(c/3)
3(-13) C -39
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Bike Repair

• Your bike needs to be fixed. A mechanic charges
  40 for each hour of labor, and the new parts
  cost 35. The total cost of fixing the bicycle in
  95. How long did it take the mechanic to fix the
  bicycle?

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Your Turn

• 9y 4 -14
• e/9 3 3
• 3(x 1) 12
• -77 -t 55
• 3/8w 14 10
• You jog at a speed of 6 miles per hour for 20
  minutes, and you walk at a speed of 4 miles per
  hour for t minutes. If your combined jogging
  walking distance is 3 miles, for how long did you
  walk?

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7.5 Concept Check

• Describe how to solve the equation
• 3x 2 13.

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7.6 Daily Puzzler

• You have drawn a circle of radius 2 feet in the
  sand on the beach. Describe the set of all points
  that are 1 foot from this circle.

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Add to your definition Sheet

• Pg 346
• Inequality
• Solution of an inequality
• Graph of an inequality
• Equivalent inequalities

Pg 350 Function input output domain Range Pg
355 Linear function
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Graphing inequalities

• X lt 2 all s less than 2
• X -1 all s less than or to -1
• X gt 0 all s greater than 0
• X -2 all s greater than or to -2

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Solving Inequalities

• D 2 1
• D 2 2 1 2
• D 3

-4w lt 20 -4w lt 20 -4 -4 W gt -5 Reverse
inequality when dividing by a negative
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Your turn

• A -12
• p 7 lt 13
• x/9 1/3
• -27n lt -108
• Z 8.6 gt 16.4
• 3 6x 21
• 2b 13 gt 9

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7.6 Concept Check

• Solve -4x gt 24 and 4x gt -24. For which inequality
  must you invert the sign?

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7.7 Daily Puzzler

• What are the next three numbers in the sequence
  1, 3, 4, 7, 11,? Explain.

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Evaluating a Function

• Evaluate y 5x when x 7
• Y 5(7)
• Y 35
• Evaluate y 2x when x -3
• Y 2(-3)
• Y -6

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Making an Input-Output Table

• Make an input-out put table for the function y
  x -1.3 using the domain 0, 1,2, 3. Then state the
  range of the function.
• The range of the function is the set of outputs
  -1.3, -0.3, 0.7, and 1.7.

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Writing a Function Rule

• Write a function rule for the table.
• You get the output by adding 2.5 to the input.
• The function rule is y x 2.5

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Your turn

• Evaluate the function y 3x 2 for the given
  value of x.
• 4
• -3
• Make an input-output table for the function using
  the domain -2, -1, 0, 1, and 2. Then state the
  range of the function.
• 3. Y x 11 4. Y 3.7x 5. Y 15 - 2x
• Write a function rule for the table
• 6.

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7.7 Concept Check

• How does input and output relate to the domain
  and range?

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7.8 Daily Puzzler

• What is the next term of the sequence 1, 2, 5,
  26, 677? Explain.

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Fabric

• You are in a craft shop, choosing fabric for a
  sewing project. The fabric you choose costs 2.50
  for each yard. How can you use a graph to
  represent this situation?

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7.8 Concept Check

• What is a linear function?