Solving Absolute Value Equations and Inequalities 1.7

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Solving Absolute Value Equations and Inequalities
1.7

• The absolute value car ride.

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• What is absolute value?
• What symbol is used to show absolute value?
• How do you transform an absolute value inequality
  and know you have the signs going in the right
  direction?

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Your house is located on 0 Number Line Drive.
If you are going to leave your house and go 3
miles, you could drive in either direction. If
you traveled East 3 miles you would end up at 3
Number Line Drive and if you traveled West 3
miles you would end up at -3 Number Line Drive.
Therefore, x3 x3.
-10 -5 0
5 10
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Absolute Value

• The absolute value of a number x, written x, is
  the distance the number is from 0 on a number
  line. The absolute value of a number is always
  nonnegative.

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Solving an absolute value equation.

• The absolute value equation axb c, where
  cgt0, is equivalent to the compound statement ax
  b c or ax b -c.

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Solving an Absolute Value Equation

• Solve

x7 or x-2
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Transformations of Absolute Value Inequalities

• The inequality axb lt c, where c gt 0, means
  that axb is between -c and c. This is
  equivalent to -c lt axb lt c. (Less than goes
  with and)
• The inequality axb gt c, where c gt 0, means
  that axb is beyond -c and c. This is equivalent
  to axb lt-c or axb gtc. (Greater than goes with
  or)

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Solving with less than

• Solve

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Solving with greater than

• Solve

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• A cereal manufacturer has a tolerance of 0.75
  ounce for a box of cereal that is supposed to
  weigh 20 ounces. Write and solve an absolute
  value inequality that describes the acceptable
  weights for 20 ounce boxes.
• Actual weight -ideal weight lt tolerance

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Quality control

• You are a quality control inspector at a bowling
  pin company. A regulation pin must weigh between
  50 ounces and 58 ounces, inclusive. Write an
  absolute value inequality describing the weights
  you should reject.
• Weight of pin - avg of extreme weights gt Tol.

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• What is absolute value?
• What symbol is used to show absolute value?
• How do you transform an absolute value inequality
  and know you have the signs going in the right
  direction?
• Check box on p. 51

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Assignment p. 53, 18-54 even, 68, 74