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  1. Today’s Objectives: Get out your notebooks! You will be able to solve absolute value equations.

  2. Warm Up Solve the following equations.

  3. 1.4 Solving Absolute Values Find the distance between the following two points on the real number line. -5 -4 -3 -2 -1 0 1 2 3 4 5

  4. Distance The distance between two real numbers is the absolute value of their ___________.

  5. Distance Statements Rewrite the absolute value statements as distance statements. is the same as saying “the distance between ____ and ____.” is the same as saying “the distance between ____ and ____.”

  6. Distance Statements Rewrite the absolute value statements as distance statements. is the same as saying “the distance between ____ and ____.” is the same as saying “the distance between ____ and ____.”

  7. Distance Therefore, distances are always positive because an absolute value is always positive.

  8. Scenario Sarah’s height is inches and Jessica’s height is inches. Their father wants to know how many inches separate his two daughters. Write an equation for this difference in such a way that the result will always be positive no matter which sister is taller.

  9. Copy This Down… Sarah is at mile marker 44. She is 7 miles from her exit. At what mile marker could Sarah’s exit be located?

  10. Scenario Make a visual representation on a number line of “the distance from mile marker 44 to Sarah’s exit x is 7.” Expanded solution: How might we write a mathematical equation for this visual representation?

  11. Examples Write a sentence in words, draw a graph, and identify the solutions. words: the distance from to is _____. ______ or ______ -5 -4 -3 -2 -1 1 2 3 4 5 0

  12. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______ -5 -4 -3 -2 -1 1 2 3 4 5 0

  13. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______ -5 -4 -3 -2 -1 1 2 3 4 5 0

  14. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______ -5 -4 -3 -2 -1 1 2 3 4 5 0

  15. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______ -5 -4 -3 -2 -1 1 2 3 4 5 0

  16. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______

  17. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______

  18. Examples Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______

  19. Generalizing words: _______________________________. Which value ( or ) is plotted first?_____ Which value tells the difference?_____ ______ or ______

  20. Word Problem Identical vacation cottages, equally spaced along a street, are numbered consecutively. Maria lives in cottage #17. Joshua lives 4 cottages away from Maria. If represents Joshua’s cottage number, then write an inequality that expresses this situation. Draw a visual representation on a number line, and solve the inequality.

  21. Examples ______ or ______

  22. Examples ______ or ______

  23. Examples ______ or ______ ______ or ______

  24. Examples ______ or ______ ______ or ______

  25. Examples

  26. Examples

  27. Examples

  28. Examples

  29. Ticket Out The Door Write an absolute value equation that corresponds to… Draw a visual representation on a number line, and Solve the equation. The carnival guesser tried to guess Aiden’s weight, but she was off by 9 pounds. Aiden actually weights 168 lbs. There are two guesses she could have made, what are they?

  30. Homework Lesson 1.4 Pg. 30 #’s 23-24, 27-32