1.6
Upcoming SlideShare
Loading in...5
×
 

1.6

on

  • 413 views

 

Statistics

Views

Total Views
413
Views on SlideShare
402
Embed Views
11

Actions

Likes
0
Downloads
8
Comments
0

1 Embed 11

http://tritonalgebra2.wikispaces.com 11

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment
  • Chang this example
  • -5<5
  • 2x+46
  • 2x+46

1.6 1.6 Presentation Transcript

  • 1.6 ABSOLUTE VALUEEQUATIONS ANDINEQUALITIESPart 1: Absolute Value Equations
  • ABSOLUTE VALUE The absolute value of a real number x, written |x|, is its distance from zero on the number line  Example:|5| =5 |-5| = 5
  • ABSOLUTE VALUES EQUATION An absolute value equation is an equation that has a variable inside the absolute value sign  Absolute value equations can have two answers because opposites have the same absolute value. View slide
  • SOLVING ABSOLUTE VALUEEQUATIONS To solve an absolute value equation: 1. Isolate the absolute value 2. Remove the absolute value signs and set up as shown: x =k x = − k or x = k 3. Check your answers! View slide
  • SOLVE EACH EQUATION.GRAPH THE SOLUTION.2x −1 = 5
  • SOLVE EACH EQUATION.GRAPH THE SOLUTION.3x + 2 = 4
  • SOLVE EACH EQUATION.GRAPH THE SOLUTION.3 x + 2 −1 = 8
  • SOLVE EACH EQUATION.GRAPH THE SOLUTION. 2 x+9 +3= 7
  • SOLVE EACH EQUATION.GRAPH THE SOLUTION.
  • EXTRANEOUS SOLUTIONS An extraneous solution is a solution derived from an original equation that is not a solution of the original equation. Remember that the absolute value measures the distance from zero on a number line. Distance can never be negative. Therefore, we must check our answers when working with absolute values.
  • SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS. x + 2 = 8x
  • SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.3x + 2 = 4 x + 5
  • SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.
  • HOMEWORK Page 46  #1 –3  #10 – 18 all  #19 – 23 odd  #43 – 51 odd
  • 1.6 ABSOLUTE VALUEEQUATIONS ANDINEQUALITIESPart 2: Absolute Value Inequalities
  • ABSOLUTE VALUE INEQUALITIES An absolute value inequality is an inequality that has a variable inside the absolute value sign.
  • SOLVING ABSOLUTE VALUEINEQUALITIES Writethe absolute value inequality as a compound inequality without absolute value symbols x < a  Compound : and x ≤ a x > a  Compound : or x ≥ a
  • Page 44
  • SOLVE AND GRAPH THE SOLUTION.2x −1 < 5
  • SOLVE AND GRAPH THE SOLUTION.3x − 4 ≤ 8
  • SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.
  • SOLVE AND GRAPH THE SOLUTION.2x + 4 ≥ 6
  • SOLVE AND GRAPH THE SOLUTION.
  • WRITE EACH COMPOUNDINEQUALITY AS AN ABSOLUTEVALUE INEQUALITY
  • HOMEWORK Page 45  #4,5  #25 – 36 all  #57 – 65 odd