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Linear Equations and Inequalities in One Variable What is an equation? =

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Linear Equations and Inequalities in One Variable What is an equation?

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Linear Equations and Inequalities in One Variable What is an equation?

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Linear Equations and Inequalities in One Variable What is an equation?

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Properties of Equality Reflexive Property a = a

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Properties of Equality Symmetric Property If a = b then b = a

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Properties of Equality Transitive Property If a = b and b = c then a = c

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Properties of Equality Addition Property If a = b then a + c = b + c

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Properties of Equality Subtraction Property If a = b then a - c = b - c

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Properties of Equality Multiplication Property If a = b then ac = bc

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Properties of Equality Division Property If a = b and c = 0 then a/c = b/c

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Properties of Equality Whatever you do to one side of an equation

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Properties of Equality do the same thing to the other side

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Properties of Equality and the two sides will stay equal

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Examples n – 6 = 9

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Examples n – 6 = 9 Add 6 to both sides (addition property)

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Examples n – 6 = 9 +6 +6

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Examples n – 6 = 9 +6 +6 n = 3

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Examples n = 3

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Examples -35 = -5r

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Examples -35 = -5r Divide both sides by -5 (division property)

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Examples -35 = -5r -5 -5

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Examples 7 = r

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Examples -3(m + 3) = 16

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Examples -3(m + 3) = 16 Distribute to get the m out of the parentheses

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Examples -3(m + 3) = 16 -3m - 9 = 16 Distribute to get the m out of the parentheses

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Examples -3(m + 3) = 16 -3m - 9 = 16 Add 9 to both sides (addition property)

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Examples -3(m + 3) = 16 -3m - 9 = 16 +9 +9

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Examples -3(m + 3) = 16 -3m - 9 = 16 +9 +9 -3m = 25

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Examples -3(m + 3) = 16 -3m - 9 = 16 +9 +9 -3m = 25 Divide both sides by -3 (division property)

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Examples -3m = 25 -3 -3

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Examples m = -25 3

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Examples 4s + 6s = 100

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Examples 4s + 6s = 100 Combine like terms

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Examples 4s + 6s = 100 10s = 100 Combine like terms

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Examples 4s + 6s = 100 10s = 100 Divide each side by 10 (division property)

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Examples 4s + 6s = 100 10s = 100 10 10

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Examples s = 10

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Examples 12 + 2g = 4 + 6g

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Examples 12 + 2g = 4 + 6g Move the variable to one side of the equation

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Examples 12 + 2g = 4 + 6g -2g -2g (subtraction property)

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Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g

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Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g Subtract 4 from both sides (subtraction property)

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Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g

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Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g Divide both sides by 4

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Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g 4 4

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Examples 2 = g

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Today’s Work: Page 45 Problems 7-20 When you finish, you may work quietly on any homework you have.

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