1.3 Open Sentences A mathematical statement with one or more variables is called an open sentence....
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Transcript of 1.3 Open Sentences A mathematical statement with one or more variables is called an open sentence....
1.3 Open Sentences
• 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• An open sentence is neither true nor false until the variables have been replaced by specific values.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.
Open Sentences
• This replacement value is called a solution of the open sentence.
• A sentence that contains an equals sign, = , is called an equation.
• 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.
Open Sentences
• Each object or number in the set is called an element.
• The solution set of an open sentence is the set of elements from the replacement set that make an open sentence true.
Use a Replacement Set to Solve an Equation• Find the solution set for each equation if the
replacement set is {3, 4, 5, 6, 7}.a. 6n + 7 = 37
Since n = 5 makes the equation true, the solution 6n + 7 = 37 is 5. The solution set is {5}.
Use a Replacement Set to Solve an Equation• Find the solution set for each equation if the
replacement set is {3, 4, 5, 6, 7}.b. 5(x + 2) = 40
The solution set is {6}.
Use Order of Operations to Solve an Equation• Solve the following equation.
13 2(4)
3(5 4)q
13 8
3(1)q
21
3q 7 q
Solve Inequalities
• An open sentence that contains the symbol < , ≤ , > , or ≥ is called an inequality.
• Inequalities can be solved the same way as equations.
Find the Solution Set of an Inequality• Find the solution set for 18 – y < 10 if the
replacement set is {7, 8, 9, 10, 11, 12}.
• The solution set for 18 – y < 10 is {9, 10, 11, 12}.