Today’s Objectives:

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## Today’s Objectives:

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**Today’s Objectives:**Get out your notebooks! You will be able to solve absolute value equations.**Warm Up**Solve the following equations.**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**Distance**The distance between two real numbers is the absolute value of their ___________.**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 ____.”**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 ____.”**Distance**Therefore, distances are always positive because an absolute value is always positive.**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.**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?**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?**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**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**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**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**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**Examples**Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______**Examples**Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______**Examples**Write a sentence in words, draw a graph, and identify the solutions. words: _____________________________. ______ or ______**Generalizing**words: _______________________________. Which value ( or ) is plotted first?_____ Which value tells the difference?_____ ______ or ______**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.**Examples**______ or ______**Examples**______ or ______**Examples**______ or ______ ______ or ______**Examples**______ or ______ ______ or ______**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?**Homework**Lesson 1.4 Pg. 30 #’s 23-24, 27-32