1. 1.7: Adding Like Terms TERM: A number, a variable, or the product of the two.Ex: a, 3x, 2x, 5, CONSTANT: a term with no variable (number) Ex: 4, -1, 6, 2 COEFFICIENT: Is the numerical factor of the a term. Ex: 3x, 5w, -3s, LIKE TERMS: Term that have the same variable factors. Ex: 7a and -3a, 4x and 12x, etc..

2. 1.7: Distributive Property Let a, b and c be real numbers. ADDITION: a( b + c ) = ab + ac3( x + 5 ) = 3x + 15 ( b + c )a = ba + ca( x + 5 )3 = 3x + 15 SUBTRACTION: a( b - c ) = ab - ac3( x - 5 ) = 3x - 15 ( b - c )a = ba - ca( x - 5 )3 = 3x - 15

3. Using Tiles and Models The area is an example of distributive property 2 4 5 Area = b ∙ h Area = 8 ∙ (2 + 5) = 2(4) + 2(5) = 8+10 = 18 u 2 Using Algebra we now have the following problem: 2 Area = b ∙ h Area = 2 ∙ (4 + x) = 2(4)+ 2(x) = 2x + 8 u 2 4 x

4. Ex: What is the simplified form of: - ( -2y – 3x)? Solution: Using the distributive property we have: - 1(2y – 3x) = -1(2y) -1(-3x) = - 2y + 3x

5. Term: a number, a variable, or the product of a number and one or more variables. Like Terms: have the same variable factors. Ex: Simplify: 2n + 1 – 4m – n + 2m Solution: Re-write as: (2n- n)+(– 4m+2m) +1 n– 2m+1

6. Class Work: Pages: 50 – 51 Problems: 9 through 63 (2x + 1)

7. 1.8: Equations Equation: A mathematical sentence that uses the equal ( = ) sign. Ex: 3x=12, -1(x + 5) = 8, Open Sentence: An equation that contains one or more variables. Ex: 3x+ 7 = 21, 2y -5 = y + 8 Solution: The value of the variable that makes the equation true. Ex: 3x+5 = 20  3x = 20-5  x = 15/3 x = 5

8. Identifying solutions: Ex: Decide if the given number is a solution: 5b + 1 = 16; -3 Solution: To show if b=3 is a solution, we must substitute: 5( -3 ) + 1 = 16 -15 + 1 = 16 –14= 16 Since -14 is not equal to 16, b=-3 is not a solution to the equation.

9. Identifying solutions: We must be able to show if a digit is a solution to an equation. Ex: is m = ½ a solution to 6m – 8 = -5? Solution: To show if m= ½ is a solution, we must substitute: 6( ½ ) – 8 = –5 3– 8 = –5 – 5 = –5 Since -5 is equal to -5, m=½ is a solution to the equation.

10. Solving Equations: To solve an equation we must ISOLATE the variable involved by using opposite math operations to the ones the equation has. Ex: Find the solution to the equations: a) 2x - 3 = 11 b) x + 4 = - 2 Solution: a) 2x – 3 = 11 + 3 + 3 – 4 = –4 b) x + 4 = – 2 2x = 14 x = 14/2 x = 7 x = –6 Don’t forget to CHECK to make sure you got the correct solution.

11. CHECK: Replace your answer in the original equation to make sure you got the correct solution. Ex: a) 2x - 3 = 11 b) x + 4 = – 2 2(7) – 3 = 11 14 – 3 = 11 – 2 = –2 (– 6 )+ 4 = – 2 11 = 11 Both integers, the left and the right, coincide thus we have gotten the correct solution.

12. Class Work: Pages: 56 – 57 Problems: 7 through 53 (2x + 1)