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Open sentences

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  • 1. Open Sentences 1-3
  • 2. Vocabulary:
    • open sentence
    • solving an open sentence
    • solution
    • equation
    • replacement set
    • set
    • element
    • solution set
    • inequality
  • 3. A mathematical statement with one or more variables is called an open sentence .  An open sentence is neither true nor false until the variables have been replaced by specific values.  The process of finding a value for a variable that results in a true sentence is called solving the open sentence .  This replacement value is called a solution of the open sentence.  A sentence that contains an equals sign, =, is called an equation .
  • 4. A set of numbers from which replacements for a variable may be chosen is called a replacement set .  A set is a collection of objects or numbers.  It is often shown using braces, { }, and is usually named by a capital letter.  Each object or number in the set is called an  element , or member.  The solution set of an open sentence is the set of elements from the replacement set that make an open sentence true.
  • 5. Use a replacement set to solve an equation
    • Find the solution set for each equation if the replacement set is {2,3,4,5,6}.
    • a.  4a + 7 = 23
    • b.  3(8 - b) = 6
  • 6. Use Order of Operations to solve an equation
    • a.           5(8 + 2)
    •           18 - (5 - 3)^3
  • 7. An open sentence that contains the symbol <, < , >, > is called an inequality .  Inequalities can be solved in the same way as equations.
  • 8. Solution set of an inequality
    • a.  Find the solution set for z + 11 > 32, if the replacement set is {20,21,22,23,24}. 
  • 9. Outdoors Ex.
    • A four-wheel drive tour of Canyon de Chelly National Monument in Arizona cost $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?
  • 10. Glencoe/McGraw-Hill 2003