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1.4 – Solving Absolute Value Equations. Absolute Value

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Text of 1.4 – Solving Absolute Value Equations. Absolute Value

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  • 1.4 Solving Absolute Value Equations
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  • Absolute Value
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs)
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5|
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| =
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 +
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3)
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7|
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 +
  • Slide 19
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15
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  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7|
  • Slide 21
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4
  • Slide 22
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 +
  • Slide 23
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22|
  • Slide 24
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4
  • Slide 25
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 +
  • Slide 26
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 + 22
  • Slide 27
  • 1.4 Solving Absolute Value Equations Absolute Valueunit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y 7| if y=-3 1.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 + 22 = 23.4
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  • Example 2
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  • Example 2 Solve |x 18| = 5.
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  • |x 18| = 5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 x = 23
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0.
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0
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  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9
  • Slide 45
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9
  • Slide 46
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note:
  • Slide 47
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!
  • Slide 48
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!
  • Slide 49
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!
  • Slide 50
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!
  • Slide 51
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!
  • Slide 52
  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x 6| + 9 = 0. |5x 6| + 9 = 0 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number! x =
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  • Example 4
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  • Example 4 Solve |x + 6| = 3x 2.
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  • |x + 6| = 3x 2
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2)
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2)
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6
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  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 =
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  • Exa