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

5

5x

5

20

5x = 20 5 · 4 = 20

20 = 20

Check:

Solving Division Equations

Solve the equation

= 3

Solving a Division Equation

7

x

Solve the equation:

= 3

7 · = 3 · 7

x = 21

Solving a Division Equation

7

x

7

x

Check the solution:

= 3 = 3 3 = 3

Check the Division Equation

7

x

7

21

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

3

t

3

t

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