Solving Absolute Value Equations

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Solving Absolute Value Equations Inequalities
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Absolute Value (of x)

• Symbol lxl
• The distance x is from 0 on the number line.
• Always positive
• Ex l-3l3

-4 -3 -2 -1 0 1
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Ex x 5

• What are the possible values of x?

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Solve the following

• 4-8
• 6-4
• 102
• 26-8
• -4-41

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To solve an absolute value equation

• axb c, where cgt0
• To solve, set up 2 new equations, then solve each
  equation.
• axb c or axb -c
• make sure the absolute value is by itself
  before you split to solve.

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Ex Solve 6x-3 15
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Ex Solve 2x 7 -3 8
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Abs Value Inequalities

• Absolute value inequalities can be represented by
  a conjunctions and disjunctions
• Three different ways
• xa
• X-a or xa

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AND with LESS THAN

• xlta
• AND statement
• Xgt-a AND xlta
• -altxlta

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OR with GREATER THAN

• xgta
• Xlt-a OR xgta

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Solving abs value inequalities

• Isolate the absolute value
• Rewrite as a compound inequality
• AND for less than, less than or equal to
• OR for greater than, greater than or equal to
• These abs value inequalities only have one
  variable (x) so they get graphed on a number line

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Solve

• 2x1gt5

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Solve

• 4x16gt8

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Solve

•  

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Ex Solve graph.
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Solve graph.
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Solving Absolute Value Inequalities

• axb lt c, where cgt0
• Becomes an and problem
• Changes to cltaxbltc
• axb gt c, where cgt0
• Becomes an or problem
• Changes to axbgtc or axblt-c