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Elementary Algebra Notes Section 2.2 Page 1 of 2 Section 2.2: The Multiplication Property of Equality Big Idea: To solve an equation, you must do the opposite of the order of operations. To solve an equation, you want to isolate the variable using the following steps: o Simplify both sides, if possible, by using the distributive property or by combining like terms. o Use the Addition Property of Equality to add or subtract a number (or variable term) from both sides so that the variable begins to be isolated. o Use the Multiplication Property of Equality to multiply (or divide) both sides of the equation by a number so that the variable gets more isolated. Big Skill: You should be able to solve slightly more complicated equations using the addition and multiplication properties of equality, and then check your solution. The multiplication property of equality: You can multiply (or divide) each side of an equation by the same NONZERO number without changing the solution. Algebraic statement: If A = B, then AC = BC are equivalent equations as long as C 0. Practice: Solve the following equations, then check your work. x 8 1. 2 2. 3x 21 3. 7 x 12 4. x 156 5. 4 x 16 3 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Elementary Algebra Notes Section 2.2 Page 2 of 2 9 27 6. x 2 4 7. 22.7 x 265 8. 12t 7 3t 9 20 9. 8t 10 10t 9 2 2t 3 10. 3 y 7 24 11. 2 1 1 x x x 18 5 10 20 12. Use our expression for the cost of golf clubs to find out how many games you can play if you only have $500 to spend on golf. 13. Suppose you are planning a wedding, and the reception hall costs a flat fee of $500 plus $15 per guest for food and $30 per guest for open bar. All of this has tax added on. If you have $2,000 to spend on the reception, how many guests can you invite? Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.