Download 9.1 The Addition Property of Equality Learning Objectives: 1. Use the

9.1 The Addition Property of Equality Learning Objectives: 1. Use the Addition Property of Equality to solve linear equations. 2. Simplify an equation and then use the Addition Property of Equality. 3. Write word phrases as algebraic expressions. 4. Key Vocabulary: solving, equivalent equations, addition property of equality. 1. Using the Addition and Distributive Property Definitions: 1. Linear Equation in One Variable • is an equation of the form Ax + By = C where A, B and C are any real numbers and A ≠ 0 . 2. Addition Property of Equality • If a = b , then a + c = b + c where a, b and c are any real numbers. 3. Distributive Property • a (b + c ) = ab + ac and − a (b + c ) = − ab − ac where a, b and c are any real numbers. Steps to Simplify Equations: 1. Simplify each sides of equation as much as possible. 2. If an equation contains parentheses, use the distributive property to remove the parentheses. 3. Using the proper of equality to solve the resulted equation. Example 1. Solve each equation. 1. − 8 x + 5 + 6 x = −3 x + 10 2. − 14.9 + 4a − 2.7 + 2a = 5.1 + 7 a + 1.5 1
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3. − x − = x + 2. Simplify an equation and then use the Addition Property of Equality Example 2. Solve each equation. 1. − 3(2 y − 5) − (5 y + 1) = −3 3. Writing Algebraic Expressions Algebraic Expressions‐are expressions that contain variable. Example 3. Write each algebraic expression described. 1. Two numbers have a sum of 72. If one number is x, express the other number in terms of x. 2. A 6‐foot board is cut into two pieces. If one piece is y feet long, express the other length in terms of y. 3. On a recent car trip, Raymond drove x miles on day one. On day two, he drove 170 miles more than he did on day one. How many miles, in terms of x, did Raymond drive for both days combined? ***************************************************************************************************** Read: 9.3/9.5