Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.
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Transcript of Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.
![Page 1: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/1.jpg)
Solving Linear EquationsPart I
Presented by Mr. Laws
8th Math/Algebra 1
JCMS
![Page 2: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/2.jpg)
Goal/Objective
8.EE.7 “Analyze and solve linear equations and pairs of simultaneous linear equations.
![Page 3: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/3.jpg)
Essential Question
Using math principles, how can we find that a linear equations has a solution, many solutions, or no solution?
Using math principles, how do I identify properties that proves the equality of linear equations?
![Page 4: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/4.jpg)
Properties of Equality
Addition Property of Equality
If the same number is added to both sides of an equation, the two sides remain equal. That is:If a = b, then a + c = b + cExample:a) 3 = 1+2; 3 + 2 = 1 + 2 + 2
Subtraction Property of Equality
If the same number is subtracted on both sides of an equation, the two sides remain equal. That is:If a = b, then a – c = b – c Example: 8 = 5 + 3; 8 – 2 = 5 + 3 – 2
![Page 5: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/5.jpg)
Properties of Equality
Multiplication Property of Equality
If the same number is multiplied on both sides of an equation, the two sides remain equal. That is:
Division Property of Equality
If a real number is divided by the same number on both sides of an equation, the two sides remain equal.
That is:
If a = b, which c is not equal to zero: Then,
If a = b, then, a c b c
63
2 6
2 3 22
a b
c c
Example: 3 + 1 = 4, so
3 1 4
2 2
![Page 6: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/6.jpg)
Solving Equations
To solve an equation containing a variable, you must find the value of the variable that will make the equation true. This is call the solution of the equation.
One way to solve an equation is to isolate the variable on one side of the equal sign.
By using the inverse operations, which are operations that undo one another. Addition, subtraction, multiplication, and division are inverse operations.
![Page 7: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/7.jpg)
One Step Equations
Using the Addition Property of Equality
Solve: x – 10 = 2
x – 10 = 2
+ 10 + 10
x = 12
Step 1: Using Addition Property of Equality
![Page 8: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/8.jpg)
One Step Equations
Using the Subtraction Property of Equality Solve y + 23 = 16
y + 23 = 16
- 23 - 23
y = -7
Step 1: Using the Subtraction Property of Equality
![Page 9: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/9.jpg)
One Step Equations
Using the Multiplication Property of Equality Solve:
56
n
6 656
n
Step 1: multiply each side by 6 to isolate the variable on one side of the equal sign.
30n
6 is cross reduced in to 1 by dividing
![Page 10: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/10.jpg)
One Step Equations
Using Reciprocals to Solve Equations. Solve: 3
94x
93 3
3
4
4 4x
Multiply each side by 4/3, which is the reciprocal of
¾.
12x
![Page 11: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/11.jpg)
One Step Equations
Using the Division Property of Equality Solve 4c = -96
4 9
4 4
6c Step 1: Divide each side by 4
24c
![Page 12: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/12.jpg)
Two Step Equations You can solve two steps equations using the properties of
equalities. For example:
3 6 18x -6 -6
3 12x 3 3
4x
2 4 36x +4 +4
2 40x 2 2
20x
![Page 13: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/13.jpg)
Two Step Equations
13 9
6x
-3 -3
36x
2 88
a +2 +2
108
ax 86 8
80x
16
6x 6
![Page 14: Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.](https://reader030.fdocuments.us/reader030/viewer/2022013004/56649e245503460f94b12433/html5/thumbnails/14.jpg)
In Summary
The Property of Equality provides you the principles to solve equations.
To find solution of equations you must find the value of the variable.
One way to solve equations is by using inverse operations to isolate the variable.
This is the basics for solving equations. Next we will move on to multiple step equations.
Make sure you take time to review and add any additional information about this lesson to your notes.