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1.4 – Solving Absolute Value Equations

# 1.4 – Solving Absolute Value Equations. Absolute Value

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• Slide 1
• 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 +
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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
• Slide 20
• 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 +
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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| =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
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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 |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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• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x
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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 = -3x
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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 = -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 = -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 = -3x (-2) x + 6 = 3x 2 x + 6
• Slide 68
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x
• Slide 69
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2
• Slide 70
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x
• Slide 71
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2
• Slide 72
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6
• Slide 73
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x
• Slide 74
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8
• Slide 75
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2
• Slide 76
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4
• Slide 77
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4
• Slide 78
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x - 6 -6 -2x = -8 -2 -2 x = 4
• Slide 79
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 - 6 -6 -2x = -8 -2 -2 x = 4
• Slide 80
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 -2x = -8 -2 -2 x = 4
• Slide 81
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -8 -2 -2 x = 4
• Slide 82
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 x = 4
• Slide 83
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4
• Slide 84
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1
• Slide 85
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1
• Slide 86
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1
• Slide 87
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1
• Slide 88
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1
• Slide 89
• Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2 x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2) x + 6 = 3x 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1

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