Download 2.1 Linear Equations: The addition and Multiplication Properties of

2.1 Linear Equations: The addition and Multiplication Properties of Equality Learning Objectives: 1. Determine if a number is a solution of an equation. 2. Use the Addition Property of Equality to solve linear equations. 3. Use the Multiplication Property of Equality to solve linear equations. 1. Determine if a number is a solution of an equation Definition: 1. A linear equation in one variable is an equation of the form ________________________________ where a, b and c are real numbers and a ≠ 0 . 2. The ______________________of a linear equation is the value or values of the variable that make the equation a ______________statement. 3. The set of all solutions of an equation is called the______________________________. Example 1. Determine if the given value of the variable is a solution of the equation 2 x + 3 = 17 a) x = −3 b) x = 7 2. Use the Addition Property of Equality to solve linear equations Addition Property of Equality: For any real numbers a, b and c Example 2. Solve the linear equation: 4 6
x+ = 3 7
1
Example 3. The total cost for purchasing an MP3 player including a sales tax of $4.47 was $78.96. Find the price p of the MP3 player by solving p + 4.47 = 78.96 . 3. Use the Multiplication Property of Equality to solve linear equations Multiplication Property of Equality: For any real numbers a, b, c and c ≠ 0 Example 4. Solve the linear equation: 1. − 6 x = 15 2. −
p
= −12 4
3. −
10
5
=− k 3
6
2