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MA.6.A.2.2

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Use algebra tiles to solve x + 2 = 4

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Use algebra tiles to solve x + 2 = 4 + =

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Use algebra tiles to solve x + 2 = 4 + = = x = 2

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To solve an addition equation, subtract the same number from each side so that the variable is by itself on one side (isolated). This process is called using the inverse operation (subtraction is the inverse or opposite operation of addition).

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Use inverse operations to solve y + 25 = 140

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Use inverse operations to solve y + 25 = 140 y + 25 = 140 - 25 -25 y = 115

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Check your answer: y + 25 = 140 115 + 25 = 140 140 = 140

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You buy an outfit at a vintage shop that costs $17.45. You pay with a $20 bill. What is the amount of change c that the clerk should give you?

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SOLUTION: Cost + Change = Amount paid Write a verbal model

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SOLUTION: Cost + Change = Amount paid Write a verbal model 17.45 + c = 20.00 Write an equation

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SOLUTION: Cost + Change = Amount paid Write a verbal model 17.45 + c = 20.00 Write an equation - 17.45 -17.45 c = 2.55 Simplify

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Check your answer: 17.45 + c = 20.00

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Check your answer: 17.45 + c = 20.00 17.45 + 2.55 = 20.00

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Check your answer: 17.45 + c = 20.00 17.45 + 2.55 = 20.00 20.00 = 20.00

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Solving Subtraction Equations

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Collecting Example: You gave away 2 conch shells from your collection and now you have 5 conch shells left. How many conch shells did you have at the start? An equation that represents this situation is x – 2 = 5, where x is the number of conch shells you had in your collection at the start.

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After giving away 2 conch shells, you have 5 conch shells. x – 2 = 5 To find the value x you had before subtracting 2, you can add 2 to undo the subtraction. 5 + 2 = x x = 7 Check: x – 2 = 5 7 -2 = 5 5 = 5

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To solve a subtraction equation, add the same number to each side so that the variable is by itself on one side (isolated). This process is called using the inverse operation (addition is the inverse or opposite operation of subtraction).

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Solve the equation: 14 = n - 6

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14 = n - 6 + 6 + 6

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Solve the equation: 14 = n - 6 14 = n - 6 + 6 + 6 20 = n

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Check your answer: 14 = n - 6 14 = n - 6 14 = 20 – 6

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Check your answer: 14 = n - 6 14 = n - 6 14 = 20 – 6 14 = 14

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Solve the equation: m – 3.1 = 11.95

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m – 3.1 = 11.95 + 3.1 + 3.1 m = 15.05

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Check your answer: m – 3.1 = 11.95 m – 3.1 = 11.95 15.05 – 3.1 = 11.95 11.95 = 11.95

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Elevator Example: You are riding an elevator. You go down 14 floors and exit on the 23 rd floor. On what floor did you enter the elevator?

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Let f represent the number of the floor on which you entered the elevator. f – 14 = 23

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Let f represent the number of the floor on which you entered the elevator. f – 14 = 23 + 14 +14 f = 37

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Check your answer: f – 14 = 23

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Check your answer: f – 14 = 23 37 – 14 = 23

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Check your answer: f – 14 = 23 37 – 14 = 23 23 = 23

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Solving Multiplication and Division Equations

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To solve an equation, try to get the variable by itself on one side of the equation. You can use inverse operations to undo the process in order to isolate the variable. To solve a multiplication equation, divide each side by the number that the variable is multiplied by. To solve a division equation, multiply each side by the divisor.

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Draw a model of the equation: 2x = 6

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= D ivide the x-tiles into 2 equal =groups. Divide the 1-tiles into the same number of equal groups. = Match a group on the left with a group on the right.

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Solve and check the equation 5x = 20

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5x = 20Write the original equation = Divide each side by 5 x = 4 Simplify

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5x = 20 5 · 4 = 20 20 = 20

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Solve the equation = 3

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Solve the equation: = 3 7 · = 3 · 7 x = 21

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Check the solution: = 3 3 = 3

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Cheerleading: In a local cheerleading competition, a team is awarded points in 3 categories. The mean of the teams scores for the 3 categories is 21. Write and solve a division equation to find t, the total number of points the team earns.

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= 21 3 · = 21 · 3 t = 63

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Estimate: 3 · 21 = 63

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Which operation(s) would you use to solve the equation below? 2x + 4 = 26

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Bell Ringer 2. Systems of Equations 4 A system of equations is a collection of two or more equations with a same set of unknowns A system of linear equations.

Bell Ringer 2. Systems of Equations 4 A system of equations is a collection of two or more equations with a same set of unknowns A system of linear equations.

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