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• Chang this example
• -5&lt;2x-1&lt;5
• 2x+4&lt;-6 or 2x+4&gt;6
• 2x+4&lt;-6 or 2x+4&gt;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