P'6 Solving Inequalities Algebraically and Graphically

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P.6 Solving Inequalities Algebraically and
Graphically

• Pgs. 53 - 62

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Solving Absolute Value Inequalities

• All absolute value inequalities represent
  compound (and/or) inequalities.
• If the original sign is lt or , you will have a
  compound and inequality.
• If the original sign is gt or , you will have a
  compound or inequality.

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Example 1

• Solve x 6 9
• Since we have , the word is and
• x 6 9 and x 6 -9
• x 15 and x -3

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Example 2

• Solve 2x 3gt 13
• Since we have gt, the word is or
• 2x 3 gt 13 or 2x 3 lt -13
• 2x gt 16 or 2x lt -10
• x gt 8 or x lt -5

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Example 3Solving Inequalities Algebraically

• Solve x2 x 12 gt 0
• x2 x 12 0 (Set the equation 0)
• (x 4)(x 3) 0 (Factor)
• x 4 0 x 3 0 (Set each factor 0)
• x 4 x -3 (Solve)

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• Plot both solutions on a number line
• Choose a number in each interval and plug into (x
  4)(x 3) to determine whether the interval is
  positive or negative.
• For x -4, (-4 4)(-4 3) is positive.
• For x 0, (0 4)(0 3) is negative.
• For x 5, (5 4)(5 3) is positive.

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• Since we want x2 x 12 gt 0, we want to choose
  the positive intervals.
• The answer is .

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You Try! ?

• Solve x2 x 6 0

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Example 4Solving Inequalities Graphically

• Solve 4x2 -12x 7 lt 0

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You Try! ?

• Solve x3 x2 6x 0