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 An open sentence is neither true nor false until the variables have been replaced by specific values.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}. 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.

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}.