1. 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.

2. Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5,, and 3.2, are also like terms. Like Terms Unlike Terms 3x and 2x 5x 2 and 2x The exponents are different. 3.2 and n Only one term contains a variable 6a and 6b The variables are different w and w7w7 5 and 1.8

3. Identify like terms in the list. Identifying Like Terms 3t 5w 2 7t 9v 4w 2 8v Look for like variables with like powers. 3t 5w 2 7t 9v 4w 2 8v Like terms: 3t and 7t 5w 2 and 4w 2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

4. Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. Simplifying Algebraic Expressions A. 6t – 4t 6t – 4t 2t2t 6t and 4t are like terms. Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

5. C. 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 5a 2 + b + 11b 2 – 6 Identify like terms. Add or subtract the coefficients. (3a 2 + 2a 2 ) + (5b – 4b) + 11b 2 – 6 Group like terms. Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

6. Simplifying Algebraic Expressions D. 4x 2 + 4y + 3x 2 – 4y + 2x 2 + 5 9x 2 + 5 Identify like terms. Add or subtract the coefficients. 4x 2 + 4y + 3x 2 – 4y + 2x 2 + 5 Group like terms. (4x 2 + 3x 2 + 2x 2 )+ (4y – 4y) + 5 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

7. 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.

8. Solve 8x + 12 - 7x = 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. - 12 -12 x = 16

9. Solve 2y - 7 + 5y = 0 Example 2 Use the Commutative Property of Addition. 2y - 7 + 5y = 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. + 7 +7 7y = 7 7 7 y = 1 Since y is multiplied by 7, divide both sides by 7 to undo the multiplication.

10. 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.

11. Solve 8x – 21 - 5x = –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. + 21 +21 3x = 6 x = 2 Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.