lesson 2.2: solving equations using addition and subtraction algebra 1 cp mrs. mongold

Lesson 2.2: Solving Lesson 2.2: Solving Equations Using Addition Equations Using Addition and Subtractionand SubtractionAlgebra 1 CPMrs. Mongold

Solving an equationSolving an equation

To solve an equation means to find all values of the variable that make it true

Solving an equationSolving an equation

To solve an equation means to find all values of the variable that make it true

Steps to solve an equation:

Solving an equationSolving an equation

To solve an equation means to find all values of the variable that make it true

Steps to solve an equation:◦1. Get the variable on one side of the

equation and get the numbers on the other side

Solving an equationSolving an equation

To solve an equation means to find all values of the variable that make it true

Steps to solve an equation:◦ 1. Get the variable on one side of the

equation and get the numbers on the other side

◦ 2. Check your answer in the original equation to make sure it makes sense

Addition Property of Addition Property of Equality:Equality:

◦If you add the same amount to each side of the equal sign, the equation is true

Addition Property of Addition Property of Equality:Equality:

◦If you add the same amount to each side of the equal sign, the equation is true Think to yourself to “undo”

subtraction you do it’s opposite which is addition

Addition Property of Addition Property of Equality:Equality:

◦If you add the same amount to each side of the equal sign, the equation is true Think to yourself to “undo”

subtraction you do it’s opposite which is addition

Ex: m – 48 = 29

Subtraction Property of Subtraction Property of Equality:Equality:

◦If you subtract the same amount from each side, the equation is true

Subtraction Property of Subtraction Property of Equality:Equality:

◦If you subtract the same amount from each side, the equation is true Think to yourself to “undo” addition you

do the opposite which is subtraction

Subtraction Property of Subtraction Property of Equality:Equality:

◦If you subtract the same amount from each side, the equation is true Think to yourself to “undo” addition you

do the opposite which is subtraction

Example: 42 + d = 27

Your turnYour turn

Solve each equation1. x+5 = 7

Your turnYour turn

Solve each equation1. x+5 = 7

Your turnYour turn

Solve each equation1. x+5 = 7 -5 -5

Your turnYour turn

Solve each equation1. x+5 = 7 -5 -5 x = 2

Your turnYour turn

Solve each equation1. x+5 = 7 -5 -5 x = 2

CHECK: 2 + 5 = 7

Your turnYour turn

Solve each equation2. x + 3 = -4

Your turnYour turn

Solve each equation2. x + 3 = -4

Your turnYour turn

Solve each equation2. x + 3 = -4 -3 -3

Your turnYour turn

Solve each equation2. x + 3 = -4 -3 -3

x = -7

Your turnYour turn

Solve each equation2. x + 3 = -4 -3 -3

x = -7

CHECK: - 7 + 3 = - 4

Your turnYour turn

Solve each equation3. x + 7 = 2

Your turnYour turn

Solve each equation3. x + 7 = 2

How do I “undo” addition?

Your turnYour turn

Solve each equation3. x + 7 = 2 -7 -7

How do I “undo” addition?

Your turnYour turn

Solve each equation3. x + 7 = 2 -7 -7

x = -5

How do I “undo” addition?

Your turnYour turn

Solve each equation3. x + 7 = 2 -7 -7

x = -5

CHECK: - 5 + 7 = 2

How do I “undo” addition?

Your turnYour turn

Solve each equation4. 32 = r – 8

Your turnYour turn

Solve each equation4. 32 = r – 8

How do I “undo” subtraction?

Your turnYour turn

Solve each equation4. 32 = r – 8 +8 = + 8 How do I “undo”

subtraction?

Your turnYour turn

Solve each equation4. 32 = r – 8 +8 = + 8

40 = r

How do I “undo” subtraction?

Your turnYour turn

Solve each equation4. 32 = r – 8 +8 = + 8

40 = r

CHECK: 32 = 40 - 8

How do I “undo” subtraction?

Your turnYour turn

Solve each equation5. 7 = 42 + t

Your turnYour turn

Solve each equation5. 7 = 42 + t

How do I move the 42? Is it being added

or subtracted or something else?

Your turnYour turn

Solve each equation5. 7 = 42 + t

It’s positive so it’s like adding…. To “undo”

addition we will subtract!!

Your turnYour turn

Solve each equation5. 7 = 42 + t -42 -42

It’s positive so it’s like adding…. To “undo”

addition we will subtract!!

Your turnYour turn

Solve each equation5. 7 = 42 + t -42 -42

-35 = t

It’s positive so it’s like adding…. To “undo”

addition we will subtract!!

Your turnYour turn

Solve each equation5. 7 = 42 + t -42 -42

-35 = t t = -35

It’s positive so it’s like adding…. To “undo”

addition we will subtract!!

What property is this?

Your turnYour turn

Solve each equation5. 7 = 42 + t -42 -42

-35 = t t = -35

It’s positive so it’s like adding…. To “undo”

addition we will subtract!!

What property is this? - Symmetric

Your turnYour turn

Solve each equation5. 7 = 42 + t -42 -42

-35 = t t = -35

CHECK: 7 = 42 + (- 35)

It’s positive so it’s like adding…. To “undo”

addition we will subtract!!

What property is this? - Symmetric

Your turnYour turn

Solve each equation6. h – 12 = -27

Your turnYour turn

Solve each equation6. h – 12 = -27

How do I “undo” subtraction?

Your turnYour turn

Solve each equation6. h – 12 = -27 +12 +12

How do I “undo” subtraction?

Your turnYour turn

Solve each equation6. h – 12 = -27 +12 +12 h = -15

How do I “undo” subtraction?

Your turnYour turn

Solve each equation6. h – 12 = -27 +12 +12 h = -15

CHECK: -15 -12 = -27

How do I “undo” subtraction?

Your turnYour turn

Solve each equation7. 4

1

2

3x

Your turnYour turn

Solve each equation7. 4

1

2

3x

How do I “undo” subtraction?

Your turnYour turn

4

1

2

3x

How do I “undo” subtraction?

Your turnYour turn

4

1

2

3x

How do I “undo” subtraction?

2

3

4

1x

Oh no! A fraction…. Are we scared?

Your turnYour turn

4

1

2

3x

How do I “undo” subtraction?

2

3

4

1x Oh no! A fraction…. Are we scared?

NO… fractions aren’t scary, like denominatorsMake this one easy to solve

Your turnYour turn

4

1

2

3x

How do I “undo” subtraction?

2

3

4

1x Oh no! A fraction…. Are we scared?

NO… fractions aren’t scary, like denominatorsMake this one easy to solve

4

6

4

1x

Your turnYour turn

4

1

2

3x

How do I “undo” subtraction?

2

3

4

1x Oh no! A fraction…. Are we scared?

NO… fractions aren’t scary, like denominatorsMake this one easy to solve

4

6

4

1x

4

5x

Your turnYour turn

4

1

2

3x

How do I “undo” subtraction?

2

3

4

1x Oh no! A fraction…. Are we scared?

NO… fractions aren’t scary, like denominatorsMake this one easy to solve

4

6

4

1x

4

5x

CHECK:

4

1

2

3

4

5

4

1

4

6

4

5

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