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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or more variables is called an open sentence .Â  An open sentence is neither true nor false until the variables have been replaced by specific values.Â  The process of finding a value for a variable that results in a true sentence is called solving the open sentence .Â  This replacement value is called a solution of the open sentence.Â  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 .Â  A set is a collection of objects or numbers.Â  It is often shown using braces, { }, and is usually named by a capital letter.Â  Each object or number in the set is called anÂ  element , or member.Â  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.Â  4a + 7 = 23
• b.Â  3(8 - b) = 6
• 6. Use Order of Operations to solve an equation
• a.Â  Â Â  Â Â Â  Â  5(8 + 2)
• Â  Â Â  Â Â Â Â  18 - (5 - 3)^3
• 7. An open sentence that contains the symbol <, < , >, > is called an inequality .Â  Inequalities can be solved in the same way as equations.
• 8. Solution set of an inequality
• a.Â  Find the solution set for z + 11 > 32, if the replacement set is {20,21,22,23,24}.Â
• 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.Â  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