1.6

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  • Chang this example
  • -5<2x-1<5
  • 2x+4<-6 or 2x+4>6
  • 2x+4<-6 or 2x+4>6
  • 1.6

    1. 1. 1.6 ABSOLUTE VALUEEQUATIONS ANDINEQUALITIESPart 1: Absolute Value Equations
    2. 2. 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
    3. 3. 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.
    4. 4. 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!
    5. 5. SOLVE EACH EQUATION.GRAPH THE SOLUTION.2x −1 = 5
    6. 6. SOLVE EACH EQUATION.GRAPH THE SOLUTION.3x + 2 = 4
    7. 7. SOLVE EACH EQUATION.GRAPH THE SOLUTION.3 x + 2 −1 = 8
    8. 8. SOLVE EACH EQUATION.GRAPH THE SOLUTION. 2 x+9 +3= 7
    9. 9. SOLVE EACH EQUATION.GRAPH THE SOLUTION.
    10. 10. 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.
    11. 11. SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS. x + 2 = 8x
    12. 12. SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.3x + 2 = 4 x + 5
    13. 13. SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.
    14. 14. HOMEWORK Page 46  #1 –3  #10 – 18 all  #19 – 23 odd  #43 – 51 odd
    15. 15. 1.6 ABSOLUTE VALUEEQUATIONS ANDINEQUALITIESPart 2: Absolute Value Inequalities
    16. 16. ABSOLUTE VALUE INEQUALITIES An absolute value inequality is an inequality that has a variable inside the absolute value sign.
    17. 17. 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
    18. 18. Page 44
    19. 19. SOLVE AND GRAPH THE SOLUTION.2x −1 < 5
    20. 20. SOLVE AND GRAPH THE SOLUTION.3x − 4 ≤ 8
    21. 21. SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.
    22. 22. SOLVE AND GRAPH THE SOLUTION.2x + 4 ≥ 6
    23. 23. SOLVE AND GRAPH THE SOLUTION.
    24. 24. WRITE EACH COMPOUNDINEQUALITY AS AN ABSOLUTEVALUE INEQUALITY
    25. 25. HOMEWORK Page 45  #4,5  #25 – 36 all  #57 – 65 odd

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