Warm Up Simplify each expression. 1.10c + c 2. 5m + 2(2m – 7) 11c 9m – 14

Algebra Basics – The Game Rules Think of algebra as a game. Objective of game: To isolate/find out what the variable is (equals). Game rules: 1.) Both sides must stay balanced at all times; whatever you do to one side of the equation, you must do to the other side (Property of Equality). 2.) We follow the order of operations backwards to “un- do” any operation on the side of the equation with the variable, and then do the same on the other side of the equation. (Variable is driver.) We “un-do” operations using their inverse. + and - are inverse operations. and ÷ are inverse operations.

Equations that are more complicated may have to be simplified before they can be solved. You may have to use the Distributive Property or combine like terms before you begin using inverse operations.

Solve 8x x = 28. Example 1: Simplifying Before Solving Equations Use the Commutative Property of Addition. 8x + 12 – 7x = 28 8x – 7x + 12 = 28 x + 12 = 28 Combine like terms. Since 12 is added to x, subtract 12 from both sides to undo the addition x = 16

Solve 2y y = 0 Example 2 Use the Commutative Property of Addition. 2y y = 0 2y + 5 y - 7 = 0 7y - 7 = 0 Combine like terms. Since 7 is subtracted from 7y, add 7 to both sides to undo the subtraction y = y = 1 Since y is multiplied by 7, divide both sides by 7 to undo the multiplication.

Solve 2a + 3 – 8a = 8. Example 3 Use the Commutative Property of Addition. 2a + 3 – 8a = 8 2a – 8a + 3 = 8 –6a + 3 = 8 Combine like terms. Since 3 is added to –6a, subtract 3 from both sides to undo the addition. – 3 – 3 –6a = 5 Since a is multiplied by –6, divide both sides by –6 to undo the multiplication.

Solve 8x – x = –15. Example 4: Simplifying Before Solving Equations Use the Commutative Property of Addition. 8x – 21 – 5x = –15 8x – 5x – 21 = –15 3x – 21 = –15 Combine like terms. Since 21 is subtracted from 3x, add 21 to both sides to undo the subtraction x = 6 x = 2 Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.