Solving Open Sentences Involving Absolute Value

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Lesson 6-5

• Solving Open Sentences Involving Absolute Value

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Objectives

• Solve absolute value equations
• Solve absolute value inequalities

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Vocabulary

• none

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Steps for Solving Equations

• Step 1 Use the Distributive Property to remove
  the grouping symbols, () or
• Step 2 Simplify the expressions on each side of
  the equal sign by combining like terms
  (variable and s)
• Step 3 Use the Addition and /or Subtraction
  Properties of Equality to get the variables on
  one side of the equal sign and the numbers
  without variables on the other side of the equals
  sign
• Step 4 Simplify the expressions on each side of
  the equals sign by combining like terms
• Step 5 Use the Multiplication and/or Division
  Properties of Equalities to solve for the variable

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Example 1
Method 1 Graphing
The distance from 6 to 11 is 5 units.
The distance from 6 to 1 is 5 units.
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Example 1 cont
Method 2 Compound Sentence
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Example 2
Write an equation involving the absolute value
for the graph.
Find the point that is the same distance from 4
as the distance from 6. The midpoint between 4
and 6 is 1.
The distance from 1 to 4 is 5 units.
The distance from 1 to 6 is 5 units.
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Example 2 cont
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Example 3
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Example 4
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Summary Homework

• Summary
• If x n, then x -n or x n
• If x lt n, then x -n or x n (inside)
• If x gt n, then x -n or x n (outside)
• Homework
• none