lesson 2.1 solving equations w/justification
DESCRIPTION
Lesson 2.1 Solving Equations w/Justification. Concept : Solving Equations EQ : How do we justify how we solve equations? REI. 1 Vocabulary : Properties of Equality Properties of Operation Justify. Solve the equations below, provide an explanation for your steps. 2x – 3 = 13. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/1.jpg)
1
Lesson 2.1 Solving Equations w/JustificationConcept: Solving Equations
EQ: How do we justify how we solve equations? REI. 1
Vocabulary:Properties of EqualityProperties of OperationJustify
![Page 2: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/2.jpg)
2
Solve the equations below, provide an explanation for your steps.1. 2x – 3 = 13
![Page 3: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/3.jpg)
Properties of Equality
2.1.1: Properties of Equality
3
Property In symbols ExampleReflexive propertyof equality a = a 2=2
Symmetric propertyof equality
If a = b, then b = a.
x = 33 = x
Transitive propertyof equality
If a = b and b = c, then a = c. x = 2, y = 2, x = y
Addition propertyof equality
If a = b, then a + c = b + c.
x – 4 = 3x – 4 + 4 = 3 + 4
x = 7
![Page 4: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/4.jpg)
Properties of Equality, continued
2.1.1: Properties of Equality
4
Property In symbols Examples
Subtractionproperty of equality
If a = b, then a – c = b – c.
x + 2 =5x + 2 – 2 = 5 – 2
x = 3
Multiplicationproperty of equality
If a = b and c ≠ 0, thena • c = b • c. x=15
Division propertyof equality
If a = b and c ≠ 0, then a ÷ c = b ÷ c.
4x = 16
x = 4
![Page 5: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/5.jpg)
Properties of Equality, continued
2.1.1: Properties of Equality
5
Property In symbols Examples
Substitutionproperty of equality
If a = b, then b may besubstituted for a in anyexpression containing a.
x = 3, then2x = 2(3) = 6
![Page 6: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/6.jpg)
Properties of Operations
2.1.1: Properties of Equality
6
Property General rule Specific exampleCommutative property of addition a + b = b + a 3 + 8 = 8 + 3
Associative property of addition
(a + b) + c = a + (b + c) (3 + 8) + 2 = 3 + (8 + 2)
Commutative property ofmultiplication a • b = b • a 3 • 8 = 8 • 3
Associative property ofmultiplication (a • b) • c = a • (b • c) (3 • 8) • 2 = 3 • (8 • 2)
Distributive property ofmultiplication over addition
a • (b + c) = a • b + a • c 3 • (8 + 2) = 3 • 8 + 3 • 2
![Page 7: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/7.jpg)
Guided PracticeExample 1Which property of equality is missing in the steps to solve the equation –7x + 22 = 50?
2.1.1: Properties of Equality
7
Equation Steps–7x + 22 = 50 Original equation
–7x = 28
x = –4 Division property of equality
![Page 8: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/8.jpg)
Guided Practice: Example 1, continued
1. Observe the differences between the original equation and the next equation in the sequence. What has changed?Notice that 22 has been taken away from both expressions, –7x + 22 and 50.
2.1.1: Properties of Equality
8
![Page 9: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/9.jpg)
Guided Practice: Example 1, continued
2. Refer to the table of Properties of Equality.The subtraction property of equality tells us that when we subtract a number from both sides of the equation, the expressions remain equal.
The missing step is “Subtraction property of equality.”
2.1.1: Properties of Equality
9
✔
![Page 10: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/10.jpg)
Guided Practice: Example 1, continued
2.1.1: Properties of Equality
10
![Page 11: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/11.jpg)
Guided Practice Example 2Which property of equality is missing in the steps to
solve the equation
2.1.1: Properties of Equality
11
Equation Steps
Original equation
Addition property of equality
–x = 42
x = –42 Division property of equality
−𝑥6 =7
![Page 12: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/12.jpg)
Guided Practice: Example 2, continued
1. Observe the differences between the original equation and the next equation in the sequence. What has changed?
Notice that 3 has been added to both expressions, and 4. The result of this step is .
2.1.1: Properties of Equality
12
![Page 13: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/13.jpg)
Guided Practice: Example 2, continuedIn order to move to the next step, the division of 6 has been undone.
The inverse operation of the division of 6 is the multiplication of 6.
The result of multiplying by 6 is –x and the result of multiplying 7 by 6 is 42. This matches the next step in the sequence.
2.1.1: Properties of Equality
13
![Page 14: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/14.jpg)
Guided Practice: Example 2, continued
2. Refer to the table of Properties of Equality.The multiplication property of equality tells us that when we multiply both sides of the equation by a number, the expressions remain equal.
The missing step is “Multiplication property of equality.”
2.1.1: Properties of Equality
14
✔
![Page 15: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/15.jpg)
Guided Practice: Example 2, continued
2.1.1: Properties of Equality
15
![Page 16: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/16.jpg)
Guided Practice: Example 3What equation is missing based on the steps?
1. Observe the 3rd and 5th equations.2. Read the 4th step.3. Fill in the missing equation.
2.1.1: Properties of Equality
16
![Page 17: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/17.jpg)
You Try…Identify the property of equality that justifies each
missing step or equation.3.
4.
17
Equation Steps9 + x = 17 Original Equation
x = 8
Equation Steps7(2x + 1) = 49 Original Equation14x + 7 = 49
14x = 42 Subtraction Property of Equality
x = 3
![Page 18: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/18.jpg)
5. Solve the equation that follows. Justify each step in your process using the properties of equality. Be sure to
include the properties of operations, if used.8(2x – 1) = 56
18
![Page 19: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/19.jpg)
Summary…Identify the property represented below.
1. x -3 = 6x - 3 + 3 = 6 + 3
2. A = B, B = C, then A = C
Solve the problem below justifying each step using the properties of equality.
3. 2x – 9 = 1
19
![Page 20: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/20.jpg)
Solving Equations with the Variable in Both Expressions of the Equation
1. Move the variable to solve for to the left of the equal sign.
2. Move all other terms to the right of the equal sign. 3. Combine like terms on each side of the equal
sign. 4. Now solve for the variable and simplify.5. Substitute the solution into the original equation
and check your work. 20
![Page 21: Lesson 2.1 Solving Equations w/Justification](https://reader036.vdocuments.us/reader036/viewer/2022062410/56816087550346895dcfafba/html5/thumbnails/21.jpg)
Example 4: Solve the equation
21