Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.
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Transcript of Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.
![Page 1: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/1.jpg)
Lesson 2.2: Solving Lesson 2.2: Solving Equations Using Addition Equations Using Addition and Subtractionand SubtractionAlgebra 1 CPMrs. Mongold
![Page 2: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/2.jpg)
Solving an equationSolving an equation
To solve an equation means to find all values of the variable that make it true
![Page 3: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/3.jpg)
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:
![Page 4: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/4.jpg)
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
![Page 5: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/5.jpg)
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
![Page 6: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/6.jpg)
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
![Page 7: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/7.jpg)
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
![Page 8: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/8.jpg)
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
![Page 9: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/9.jpg)
Subtraction Property of Subtraction Property of Equality:Equality:
◦If you subtract the same amount from each side, the equation is true
![Page 10: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/10.jpg)
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
![Page 11: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/11.jpg)
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
![Page 12: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/12.jpg)
Your turnYour turn
Solve each equation1. x+5 = 7
![Page 13: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/13.jpg)
Your turnYour turn
Solve each equation1. x+5 = 7
![Page 14: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/14.jpg)
Your turnYour turn
Solve each equation1. x+5 = 7 -5 -5
![Page 15: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/15.jpg)
Your turnYour turn
Solve each equation1. x+5 = 7 -5 -5 x = 2
![Page 16: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/16.jpg)
Your turnYour turn
Solve each equation1. x+5 = 7 -5 -5 x = 2
CHECK: 2 + 5 = 7
![Page 17: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/17.jpg)
Your turnYour turn
Solve each equation2. x + 3 = -4
![Page 18: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/18.jpg)
Your turnYour turn
Solve each equation2. x + 3 = -4
![Page 19: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/19.jpg)
Your turnYour turn
Solve each equation2. x + 3 = -4 -3 -3
![Page 20: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/20.jpg)
Your turnYour turn
Solve each equation2. x + 3 = -4 -3 -3
x = -7
![Page 21: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/21.jpg)
Your turnYour turn
Solve each equation2. x + 3 = -4 -3 -3
x = -7
CHECK: - 7 + 3 = - 4
![Page 22: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/22.jpg)
Your turnYour turn
Solve each equation3. x + 7 = 2
![Page 23: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/23.jpg)
Your turnYour turn
Solve each equation3. x + 7 = 2
How do I “undo” addition?
![Page 24: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/24.jpg)
Your turnYour turn
Solve each equation3. x + 7 = 2 -7 -7
How do I “undo” addition?
![Page 25: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/25.jpg)
Your turnYour turn
Solve each equation3. x + 7 = 2 -7 -7
x = -5
How do I “undo” addition?
![Page 26: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/26.jpg)
Your turnYour turn
Solve each equation3. x + 7 = 2 -7 -7
x = -5
CHECK: - 5 + 7 = 2
How do I “undo” addition?
![Page 27: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/27.jpg)
Your turnYour turn
Solve each equation4. 32 = r – 8
![Page 28: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/28.jpg)
Your turnYour turn
Solve each equation4. 32 = r – 8
How do I “undo” subtraction?
![Page 29: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/29.jpg)
Your turnYour turn
Solve each equation4. 32 = r – 8 +8 = + 8 How do I “undo”
subtraction?
![Page 30: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/30.jpg)
Your turnYour turn
Solve each equation4. 32 = r – 8 +8 = + 8
40 = r
How do I “undo” subtraction?
![Page 31: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/31.jpg)
Your turnYour turn
Solve each equation4. 32 = r – 8 +8 = + 8
40 = r
CHECK: 32 = 40 - 8
How do I “undo” subtraction?
![Page 32: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/32.jpg)
Your turnYour turn
Solve each equation5. 7 = 42 + t
![Page 33: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/33.jpg)
Your turnYour turn
Solve each equation5. 7 = 42 + t
How do I move the 42? Is it being added
or subtracted or something else?
![Page 34: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/34.jpg)
Your turnYour turn
Solve each equation5. 7 = 42 + t
It’s positive so it’s like adding…. To “undo”
addition we will subtract!!
![Page 35: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/35.jpg)
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!!
![Page 36: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/36.jpg)
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!!
![Page 37: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/37.jpg)
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?
![Page 38: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/38.jpg)
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
![Page 39: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/39.jpg)
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
![Page 40: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/40.jpg)
Your turnYour turn
Solve each equation6. h – 12 = -27
![Page 41: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/41.jpg)
Your turnYour turn
Solve each equation6. h – 12 = -27
How do I “undo” subtraction?
![Page 42: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/42.jpg)
Your turnYour turn
Solve each equation6. h – 12 = -27 +12 +12
How do I “undo” subtraction?
![Page 43: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/43.jpg)
Your turnYour turn
Solve each equation6. h – 12 = -27 +12 +12 h = -15
How do I “undo” subtraction?
![Page 44: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/44.jpg)
Your turnYour turn
Solve each equation6. h – 12 = -27 +12 +12 h = -15
CHECK: -15 -12 = -27
How do I “undo” subtraction?
![Page 45: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/45.jpg)
Your turnYour turn
Solve each equation7. 4
1
2
3x
![Page 46: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/46.jpg)
Your turnYour turn
Solve each equation7. 4
1
2
3x
How do I “undo” subtraction?
![Page 47: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/47.jpg)
Your turnYour turn
4
1
2
3x
How do I “undo” subtraction?
![Page 48: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/48.jpg)
Your turnYour turn
4
1
2
3x
How do I “undo” subtraction?
2
3
4
1x
Oh no! A fraction…. Are we scared?
![Page 49: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/49.jpg)
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
![Page 50: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/50.jpg)
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
![Page 51: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/51.jpg)
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
![Page 52: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/52.jpg)
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
![Page 53: Lesson 2.2: Solving Equations Using Addition and Subtraction Algebra 1 CP Mrs. Mongold.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649ec05503460f94bcae7a/html5/thumbnails/53.jpg)
HomeworkHomeworkPage 15