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Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS

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Goal/Objective 8.EE.7 “Analyze and solve linear equations and pairs of simultaneous linear equations.

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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?

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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 + c Example: 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

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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, Example: 3 + 1 = 4, so

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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.

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One Step Equations Using the Addition Property of Equality Solve: x – 10 = 2 x – 10 = 2 + 10 x = 12 Step 1: Using Addition Property of Equality

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One Step Equations Using the Subtraction Property of Equality Solve y + 23 = 16 y + 23 = 16 - 23 y = -7 Step 1: Using the Subtraction Property of Equality

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One Step Equations Using the Multiplication Property of Equality Solve: Step 1: multiply each side by 6 to isolate the variable on one side of the equal sign. 6 is cross reduced in to 1 by dividing

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One Step Equations Using Reciprocals to Solve Equations. Solve: Multiply each side by 4/3, which is the reciprocal of ¾.

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One Step Equations Using the Division Property of Equality Solve 4c = -96 Step 1: Divide each side by 4

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Two Step Equations You can solve two steps equations using the properties of equalities. For example: -6 3 3 +4 2 2

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Two Step Equations -3 +2

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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.

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