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Lesson 3 Contents Vocabularies: Open sentence – a mathematic statement with one or more variables. An open sentence is neither true nor false until the variables have been replaced by specific values. Replacement set – a set of numbers from which replacements for the variable may be chosen. Element – each number in the replacement set. Solution set – the set of elements that make an open sentence true.

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false 2 True or False? false 5 3 true 4 false 6 a Example 3-1a Find the solution set for if the replacement set is {2, 3, 4, 5, 6}. Replace a in with each value in the replacement set. Answer: The solution set is {4}.

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true 6 false 5 4 3 2 True or False? a Replace with each value in the replacement set. Find the solution set for if the replacement set is {2, 3, 4, 5, 6}. Example 3-1b Answer: The solution set is {6}.

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Example 3-1c Find the solution set for each equation if the replacement set is {0, 1, 2, 3, 4}. a. b. Answer: {2} Answer: {0}

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Example 3-2a Solve Original equation Add 8 and 2 in the numerator. Subtract 5 and 3 in the denominator. Evaluate the power in the denominator. Simplify. Answer: Divide.

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Example 3-2b Answer: 6

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true 24 true 23 true 22 true 21 false 20 True or False? a Example 3-3a Replace with each value in the replacement set. Find the solution set forif the replacement set is {20, 21, 22, 23, 24}. Answer:The solution set for is {21, 22, 23, 24}.

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Example 3-3b Find the solution set for if the replacement set is {2, 3, 4, 5}. Answer: {5}

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Example 3-4a Outdoors A four-wheel-drive tour of Canyon de Chelly National Monument in Arizona costs $45 for the first vehicle and $15 for each additional vehicle. How many vehicles can the Velo family take on the tour if they want to spend no more than $100? ExploreThe expressioncan be used to represent the cost ofvehicles. The family wants to spend no more than $100. The situation can be represented by the inequality. PlanSince no replacement set is given, estimate to find reasonable values for the replacement set.

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Example 3-4a The estimate is too high. Decrease the value of n. SolveStart by letting and then adjust values up or down as needed. Original inequality Multiply 15 and 6. Add 45 and 90.

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Example 3-4a ExamineThe solution set is {0, 1, 2, 3}. In addition to the first vehicle, the Velo family can take up to 3 additional vehicles and spend no more than $100. Answer:They can take as many as vehicles and stay within their budget. too high 4 almost 3 too low 2 too high 5 Reasonable? n

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Example 3-4b Books A mail-order Book Club is having a sale on paperback books. You can purchase an unlimited number of books for $8.50 each. There is a $7.00 charge for shipping. How many books can you buy if you have $60 to spend? Answer: 6

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End of Lesson 3

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