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1-5 Absolute Value Equations. Objectives: To solve absolute value equations. Absolute Value. What is the definition of absolute value??? Distance from zero, so it’s always _________ How many numbers are the same distance from zero? So every absolute value equation has two answers except….

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1 5 absolute value equations

1-5 Absolute Value Equations

Objectives:

To solve absolute value equations

absolute value
Absolute Value
  • What is the definition of absolute value???
    • Distance from zero, so it’s always _________
    • How many numbers are the same distance from zero?
      • So every absolute value equation has two answers except…
solving equations with absolute values
Solving Equations with Absolute Values
  • Isolate the absolute value (get rid of outside numbers)
  • Split into two equations without the absolute value symbols
  • Solve the equations

2|3x +4| - 3 = 7

examples
Examples
  • 3|5x + 6|-7 = 2 2. 8 + 5|6 - 2y| = 68
question
Question
  • Is there a solution to 2|x| = -14?
  • So if an absolute value equals a negative number, there is no solution.
definition
Definition
  • Extraneous Solution: a solution derived from a an original equation that is not a solution of the original equation.
    • It doesn’t work when you plug it in.
variables on both sides
Variables on both sides

Solve and check for extraneous solutions.

|2x + 3| = 3x + 2

examples1
Examples

|3x – 4| = –4x – 1 6|2x + 5| = 6x + 24

example
Example

⅔|3x – 6| = 4(x – 2)

homework
Homework

Page 36, #1-15 odd, 35-43odd, 61,62