 # 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? =

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

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

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

Properties of Equality Reflexive Property a = a

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

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

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

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

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

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

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

Properties of Equality do the same thing to the other side

Properties of Equality and the two sides will stay equal

Examples n – 6 = 9

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

Examples n – 6 = 9 +6 +6

Examples n – 6 = 9 +6 +6 n = 3

Examples n = 3

Examples -35 = -5r

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

Examples -35 = -5r -5 -5

Examples 7 = r

Examples -3(m + 3) = 16

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

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

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

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

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

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

Examples -3m = 25 -3 -3

Examples m = -25 3

Examples 4s + 6s = 100

Examples 4s + 6s = 100 Combine like terms

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

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

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

Examples s = 10

Examples 12 + 2g = 4 + 6g

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

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

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

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

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

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

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

Examples 2 = g

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

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