lesson 2.2: solving equations using addition and subtraction algebra 1 cp mrs. mongold
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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
HomeworkHomeworkPage 15