Warm Up 10/23/12 To become a member of an ice skating rink, you have to pay a $30 membership fee. The cost of admission to the rink is $5 for members and $7 for nonmembers. After how many visits to the rink is the total cost for members, including the membership fee, the same as the total cost for nonmembers? Write an equation and solve.

Solving Linear Equations (Flow Map) Parenthesis Distributive Property Yes Combine Like Terms (each side separately) No Solving Linear Equations (Flow Map) Box Variables Separate Sides Variables on Both Sides? Isolate Variable On One Side (Additive Inverse) Yes Move Constant To Other Side (Additive Inverse) No Isolate Variable On One Side (Multiplicative Inverse) Box Your Answer Check Your Answer! © Eugene Ruben Ramirez

is an equation that is true for all values of the variable. Topic: Solving Equations With Variables on Both Sides Essential Question: How do we solve equations with Variables on both sides Standard: 8.EE.7 Identity: is an equation that is true for all values of the variable.

Solve 1) 4x –10 = 32 – 3x 4x –10 = 32 – 3x +3x +3x 7x –10 = 32 +10 +10 Question / Key Words Notes or Solutions to Problems Solve 1) 4x –10 = 32 – 3x 4x –10 = 32 – 3x +3x +3x 7x –10 = 32 +10 +10 1 7x = 42 7 7 x = 6

5x – 2 = 3x + 6

8y + 4 = 11y - 17

m – 1 = 9m + 15

Solve 2) 6x = 5x – 33 6x = 5x – 33 –5x – 5x x = -33 Question / Key Words Notes or Solutions to Problems Solve 2) 6x = 5x – 33 6x = 5x – 33 –5x – 5x x = -33

8x = 6x - 14

Solve 3) 10x – 22 = -x 10x –22 = -x +x +x 11x –22 = +22 +22 11x = 22 Question / Key Words Notes or Solutions to Problems Solve 3) 10x – 22 = -x 10x –22 = -x +x +x 11x –22 = +22 +22 1 11x = 22 11 11 x = 2

5x + 24 = -x

Solve 2x –9 + 7x = -34 – 3x +7x 9x – 9 = 4x – 34 –4x –4x 5x – 9 = – 34 Question / Key Words Notes or Solutions to Problems Solve 4) 2x –9 + 7x = -34 – 3x +7x 2x – 9 + 7x = -34 – 3x +7x 9x – 9 = 4x – 34 –4x –4x 5x – 9 = – 34 +9 +9 1 5x = -25 5 5 x = -5

6y + 7y + 19 = 54 + 14+ 6y

is an equation that is true for all values of the variable. Topic: Solving Equations With Variables on Both Sides Essential Question: How do we solve equations with Variables on both sides Standard: 4.0 Identity: is an equation that is true for all values of the variable.

Solve 9x – (x + 6) 1 = -2(x – 6) + 5 9x –1x –6 = -2x + 12 + 5 8x –6 = Question / Key Words Notes or Solutions to Problems Solve 9x – (x + 6) 1 = -2(x – 6) + 5 5) 9x – (x + 6) = -2(x – 6) +5 9x –1x –6 = -2x + 12 + 5 8x –6 = -2x + 17 +2x +2x 10x – 6 = 17 +6 +6 1 10x = 23 10 10 3 2 x = 10

2(4x + 5) = 8x + 10 8x + 10 = 8x + 10 –8x –8x 10 = 10 Identity 6) Question / Key Words Notes or Solutions to Problems Solve the equation if possible. Determine whether it has one solution, no solution, or is an identity. 2(4x + 5) = 8x + 10 8x + 10 = 8x + 10 6) 2(4x + 5) = 8x + 10 –8x –8x 10 = 10 Answer: The equation 10 = 10 is always true, so all values of x are solutions. The original equation is an identity. Identity

x – 1 = x + 7 –x –x -1 = 7 No solution. 7) x – 1 = x + 7 Question / Key Words Notes or Solutions to Problems Solve the equation if possible. Determine whether it has one solution, no solution, or is an identity. x – 1 = x + 7 –x –x 7) x – 1 = x + 7 -1 = 7 Answer: The equation -1 = 7 is never true no matter what the value of x. The original equation has no solution. No solution.

Vocabulary of Math Operations Addition (+) Subtraction (–) Multiplication(), • Division (÷) sum difference of product quotient plus minus times divide added to subtracted from multiply into more than less than twice ratio increased by decreased by total less