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Open sentences

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Open sentences

1. 1. Open Sentences 1-3
2. 2. Vocabulary: <ul><li>open sentence </li></ul><ul><li>solving an open sentence </li></ul><ul><li>solution </li></ul><ul><li>equation </li></ul><ul><li>replacement set </li></ul><ul><li>set </li></ul><ul><li>element </li></ul><ul><li>solution set </li></ul><ul><li>inequality </li></ul>
3. 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  An open sentence is neither true nor false until the variables have been replaced by specific values.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. 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. 5. Use a replacement set to solve an equation <ul><li>Find the solution set for each equation if the replacement set is {2,3,4,5,6}. </li></ul><ul><li>a.  4a + 7 = 23 </li></ul><ul><li>b.  3(8 - b) = 6 </li></ul>
6. 6. Use Order of Operations to solve an equation <ul><li>a.           5(8 + 2) </li></ul><ul><li>          18 - (5 - 3)^3 </li></ul>
7. 7. An open sentence that contains the symbol <, < , >, > is called an inequality .  Inequalities can be solved in the same way as equations.
8. 8. Solution set of an inequality <ul><li>a.  Find the solution set for z + 11 > 32, if the replacement set is {20,21,22,23,24}.  </li></ul>
9. 9. Outdoors Ex. <ul><li>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? </li></ul>
10. 10. Glencoe/McGraw-Hill 2003