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Solving Equations MA.6.A.2.2
Solving EquationsMA.6.A.2.2
Use algebra tiles to solve x + 2 = 4
Solving Addition Equations Using Algebra Tiles
Use algebra tiles to solve x + 2 = 4
+ =
Solving Equations Using Algebra Tiles
Use algebra tiles to solve x + 2 = 4
+ =
= x = 2
Solving Equations Using Algebra Tiles
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).
Solving Addition Equations
Use inverse operations to solvey + 25 = 140
Solving Addition Equations Using Inverse
Operations
Use inverse operations to solve y + 25 = 140
y + 25 = 140 - 25 -25 y = 115
Solving Equations Using Inverse Operations
Check your answer:
y + 25 = 140115 + 25 = 140
140 = 140
Solving Equations Using Inverse Operations
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?
Using an Addition Equation
SOLUTION:
Cost + Change = Amount paid Write a verbal model
Using an Addition Equation
SOLUTION:
Cost + Change = Amount paid Write a verbal model
17.45 + c = 20.00 Write an equation
Using an Addition Equation
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
Using an Addition Equation
Check your answer:
17.45 + c = 20.00
Using an Addition Equation
Check your answer:
17.45 + c = 20.0017.45 + 2.55 = 20.00
Using an Addition Equation
Check your answer:
17.45 + c = 20.0017.45 + 2.55 = 20.00
20.00 = 20.00
Using an Addition Equation
Solving Subtraction Equations
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.
Solving Subtraction EquationsWorking Backwards
After giving away 2 conch shells, you have 5 conchshells.
x – 2 = 5To find the value x you had before subtracting 2, youcan add 2 to undo the subtraction.
5 + 2 = xx = 7
Check: x – 2 = 57 -2 = 5
5 = 5
Solving Subtraction EquationsWorking Backwards
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).
Solving Subtraction Equations
Solve the equation: 14 = n - 6
Solving Subtraction Equations Using Inverse
Operations
Solve the equation: 14 = n - 6
14 = n - 6 + 6 + 6
Solving Subtraction Equations Using Inverse
Operations
Solve the equation: 14 = n - 6
14 = n - 6 + 6 + 6 20 = n
Solving Subtraction Equations Using Inverse
Operations
Check your answer: 14 = n - 6
14 = n - 6 14 = 20 – 6
Solving Subtraction Equations Using Inverse
Operations
Check your answer: 14 = n - 6
14 = n - 6 14 = 20 – 6
14 = 14
Solving Subtraction Equations Using Inverse
Operations
Solve the equation: m – 3.1 = 11.95
Solving Subtraction Equations Using Inverse
Operations
Solve the equation: m – 3.1 = 11.95
m – 3.1 = 11.95 + 3.1 + 3.1 m = 15.05
Solving Subtraction Equations Using Inverse
Operations
Check your answer: m – 3.1 = 11.95
m – 3.1 = 11.95 15.05 – 3.1 = 11.95 11.95 = 11.95
Solving Subtraction Equations Using Inverse
Operations
Elevator Example: You are riding an elevator. You go down 14 floors and exit on the 23rd floor. On what floor did you enter the elevator?
Using a Subtraction Equation
Let f represent the number of the floor on which you entered the elevator.
f – 14 = 23
Using a Subtraction Equation
Let f represent the number of the floor on which you entered the elevator.
f – 14 = 23 + 14 +14 f = 37
Using a Subtraction Equation
Check your answer:
f – 14 = 23
Using a Subtraction Equation
Check your answer:
f – 14 = 23 37 – 14 = 23
Using a Subtraction Equation
Check your answer:
f – 14 = 23 37 – 14 = 23 23 = 23
Using a Subtraction Equation
Solving Multiplication and Division Equations
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.
Solving Multiplication and Division Equations
Draw a model of the equation:
2x = 6
Algebra Tiles Activity
=
Divide 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.
Solve using Algebra Tiles
Solve and check the equation
5x = 20
Solving a Multiplication Equation
5x = 20 Write the original equation = Divide each side by 5
x = 4 Simplify
Solve
55x
520
5x = 20 5 · 4 = 20
20 = 20
Check:
Solving Division Equations
Solve the equation
= 3
Solving a Division Equation
7x
Solve the equation:
= 3 7 · = 3 · 7
x = 21
Solving a Division Equation
7x
7x
Check the solution:
= 3 = 3 3 = 3
Check the Division Equation
7x
721
Cheerleading: In a local cheerleading competition, a team is awarded points in 3 categories. The mean of the team’s scores for the 3 categories is 21. Write and solve a division equation to find t, the total number of points the team earns.
Using an Equation
= 21 3 · = 21 · 3
t = 63
Setup and Solve the Equation
3t
3t
Estimate: 3 · 21 = 63
Check your Answer
Which operation(s) would you use to solve the equation below?
2x + 4 = 26
Solve the Two-Step Equation
