Solving Inequalities Involving Absolute Value

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• Solving Inequalities Involving Absolute Value

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Types of Open Sentences

• x 3
• -3, 3
• the distance from zero is 3
• x lt 3 intersection
• x -3 lt x lt 3
• the distance from zero lt 3
• x gt 3 union
• x x lt - 3 or x gt 3
• the distance from zero gt 3

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Cases to Consider (Positive)

• Rewrite problem without the abs value signs
• Write the expression inside the abs value signs
• Flip the ineq symbol
• Write the additive inverse of the value after the
  ineq symbol

Cases to Consider (Negative)
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Steps to Solving

• Isolate the absolute value expression
• Identify type of compound ineq
• Intersection lt ,
• Union gt ,
• Set up 2 cases
• Solve each case

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Example 1

• Solve graph x - 5 2.

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Example 2

• Solve graph 6x gt 18.

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Example 3

• Solve graph 52x - 3 25.

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Example 4

• Solve graph 7x 4 lt 0.