Algebra 1 Ch 2.4 – Solving Equations with Variables on Both Sides.
2.4 Reasoning with Properties from Algebra
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Transcript of 2.4 Reasoning with Properties from Algebra
2.4 Reasoning with 2.4 Reasoning with Properties from Properties from
AlgebraAlgebraUse properties of AlgebraUse properties of Algebra
Properties of Algebra
Addition Property
If a = b, then a + c = b + c
If x – 4 = 20, then x – 4 + 4 = 20 + 4
Properties of Algebra
Multiplication Property
If a = b, then a * c = b * c where c ≠ 0
If ⅛ x = 4, then 8 * ⅛ x = 4 * 8
Other properties in Algebra
Reflexive Property x = x
Symmetric Property
If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c
More properties in Algebra
Substitution Property
If x = 4, then 3x + 2 = 3(4) + 2
Distributive Property
2(x + 4) = 2x + 2(4)
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property
12 = 5x -18 Simplified
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property
12 = 5x -18 Simplified
18 = 18 Reflexive Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18 Add. Property
12 = 5x -18 Simplified
18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given - 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given - 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18 Add. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given - 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18 Add. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property30 * 1/5 = 5x * 1/5 Mult. Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given - 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18 Add. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property30 * 1/5 = 5x * 1/5 Mult. Property
6 = x Simplified
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given - 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18 Add. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property30 * 1/5 = 5x * 1/5 Mult. Property
6 = x Simplifiedx = 6 Symmetric Property
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ;
AC = BD Verify that AB = CD
AC = BD Given
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ;
AC = BD Verify that AB = CD
AC = BD Given
AC = AB + BC
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ;
AC = BD Verify that AB = CD
AC = BD Given
AC = AB + BC Segment Addition
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ;
AC = BD Verify that AB = CD
AC = BD Given
AC = AB + BC Segment Addition
BD = BC + CD Segment Addition
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ;
AC = BD Verify that AB = CD
AC = BD Given
AC = AB + BC Segment Addition
BD = BC + CD Segment Addition
AB + BC = BC + CD
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ;
AC = BD Verify that AB = CD
AC = BD Given
AC = AB + BC Segment Addition
BD = BC + CD Segment Addition
AB + BC = BC + CD Substitution Prop.
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ; AC = BD Verify that AB = CD
AC = BD GivenAC = AB + BC Segment AdditionBD = BC + CD Segment AdditionAB + BC = BC + CD Substitution Prop.BC = BC Reflexive Prop.
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ; AC = BD Verify that AB = CD
AC = BD GivenAC = AB + BC Segment AdditionBD = BC + CD Segment AdditionAB + BC = BC + CD Substitution Prop.BC = BC Reflexive Prop.AB = CD Addition/ Subtraction
Prop.
Given Find
#1. #1. Given
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Given Find
#1. #1. Given
#2. #2. Subst. Prop
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43321 mmmmm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
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33 mm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
#4. #4. Add./Subt Prop.
18043
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180321
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33 mm
421 mmm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
#4. #4. Add./Subt. Prop.
#5. #5. Given
18043
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180321
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33 mm
421 mmm
9321 mm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
#4. #4. Add./Subt. Prop.
#5. #5. Given
#6. #6. Substitution
18043
9321
180321
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4m
18043
180321
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43321 mmmmm
33 mm
421 mmm
9321 mm
493 m
HomeworkHomework
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