Open sentences
- 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 An open sentence is neither true nor false until the variables have been replaced by specific values.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?