Absolute Value Inequalities

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Absolute Value Inequalities
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Absolute Value

• Look at the inequality symbol in the original
  problem.
• Greater than means or.
• Less than means and.
• GOLAGreater is or, less is and

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Example 1

• 3x 1 gt 5
• Write two equationsUse or between them since
  it started out as greater than
• 3x 1 gt 5 OR 3x 1 lt -5
• Solve Add one to each side (of each)
• 3x 1 1 gt 5 1 OR 3x 1 1lt -5 1
• 3x gt 6 OR 3x lt -4
• Divide both sides by 3
• X gt 2 OR x lt -4/3
• Graph

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X gt 4/3 OR x lt -2

This is the solution.
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Example 2

• 2x 2 lt 8
• Write two equationsThese will be separated by
  and since it starts with less than or equal
  to
• 2x 2 lt 8 AND 2x 2 gt -8
• Add 2 to both sides (for each)
• 2x 2 2 lt 8 2 AND 2x 2 2 gt -8 2
• 2x lt 10 AND 2x gt -6
• Divide both sides by 2
• x lt 5 AND x gt -3

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Example 2 cont
x lt 5 AND x gt -3 means
-3 lt x lt 5
-3 0 5
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Try these

• x 2 lt 5
• 5x 4 gt 16
• x 3 lt -4

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Try theseanswers

• x 2 lt 5
• 5x 4 gt 16
• x 3 lt -4