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1.4 – Solving Absolute Value Equations

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1.4 – Solving Absolute Value Equations. 1.4 – Solving Absolute Value Equations. Absolute Value. 1.4 – Solving Absolute Value Equations. Absolute Value–unit value only. 1.4 – Solving Absolute Value Equations. Absolute Value–unit value only. 1.4 – Solving Absolute Value Equations. - PowerPoint PPT Presentation

Text of 1.4 – Solving Absolute Value Equations

  • 1.4 Solving Absolute Value Equations

  • 1.4 Solving Absolute Value EquationsAbsolute Value

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5|

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| =

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-3

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 +

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3)

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7|

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 +

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7|

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 +

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22|

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 +

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 + 22

  • 1.4 Solving Absolute Value EquationsAbsolute Valueunit value only (w/o signs)ex. |-5| = 5; |5| = 5

    Example 1 Evaluate 1.4+|5y 7| if y=-31.4+|5y 7|=1.4 + |5(-3) 7| =1.4 + |-15 7| =1.4 + |-22| =1.4 + 22 = 23.4

  • Example 2

  • Example 2 Solve |x 18| = 5.

  • Example 2 Solve |x 18| = 5. |x 18| = 5

  • Example 2 Solve |x 18| = 5. |x 18| = 5

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 x = 23

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13

  • Example 2 Solve |x 18| = 5. |x 18| = 5 x 18 = 5x 18 = -5 +18 +18 +18 +18 x = 23x = 13

    Example 3

  • 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.

  • 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

  • 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 -9

  • 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 -9 |5x 6| = -9

  • 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 -9 |5x 6| = -9 Note:

  • 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 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!

  • 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 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!

  • 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 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!

  • 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 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!

  • 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 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!

  • 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 -9 |5x 6| = -9 Note: Absolute value cannot equal a negative number!x =

  • Example 4

  • Example 4 Solve |x + 6| = 3x 2.

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2)

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2)

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 =

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x -2x + 6 = -2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x -2x + 6 = -2 - 6 -6

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x -2x + 6 = -2 - 6 -6-2x

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x -2x + 6 = -2 - 6 -6 -2x = -8

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 6 = 3x 2 x + 6 = -(3x 2) x + 6 = -3x (-2)x + 6 = 3x 2 x + 6 = -3x + 2-3x -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4 OR x = -1

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4 OR x = -1

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4 OR x = -1

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4 OR x = -1

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4 OR x = -1

  • Example 4 Solve |x + 6| = 3x 2. |x + 6| = 3x 2x + 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 4x = 4 OR x = -1