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Entry Task ? LT: I can solve equations and problems by writing equations

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1.4 Solving Equations Learning Target: I can Solve equations and solve problems by writing equations

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Vocabulary Equation Solution to an equation Inverse operation Identity Literal equation LT: I can solve equations and problems by writing equations

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●A variable is a letter which represents an unknown number. Any letter can be used as a variable. ●An algebraic expression contains at least one variable. Examples: a, x+5, 3y – 2z ●A verbal expression uses words to translate algebraic expressions. Example: “The sum of a number and 3” represents “ n+3. ” Review of Terms LT: I can solve equations and problems by writing equations

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An equation is a sentence that states that two mathematical expressions are equal. Example: 2x-16=18 Vocabulary LT: I can solve equations and problems by writing equations

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Properties of Real Numbers Reflexive Property a + b = a + b The same expression is written on both sides of the equal sign. LT: I can solve equations and problems by writing equations

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Properties of Real Numbers If a = b then b = a If 4 + 5 = 9 then 9 = 4 + 5 Symmetric Property LT: I can solve equations and problems by writing equations

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Properties of Real Numbers Transitive Property If a = b and b = c then a = c If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5 LT: I can solve equations and problems by writing equations

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Properties of Real Numbers Substitution Property If a = b, then a can be replaced by b. a(3 + 2) = b(5) LT: I can solve equations and problems by writing equations

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Name the property A. 5(4 + 6) = 20 + 30 B. 5(4 + 6) = 5(10) C. 5(4 + 6) = 5(4 + 6) D. If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6) E. 5(4 + 6) = 5(6 + 4) F. If 5(10) = 5(4 + 6) and 5(4 + 6) = 20 + 30 then 5(10) = 20 + 30 a) Distributive b) Substitution c) Reflexive d) Symmetric e) Commutative f) Transitive LT: I can solve equations and problems by writing equations

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Steps to Solving Equations I.Simplify each side of the equation, if needed, by distributing or combining like terms. II.Move variables to one side of the equation by using the opposite operation of addition or subtraction. LT: I can solve equations and problems by writing equations

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Steps to Solving Equations cont. III. Isolate the variable by applying the opposite operation to each side. I.First, use the opposite operation of addition or subtraction. II.Second, use the opposite operation of multiplication or division. IV. Check your answer. LT: I can solve equations and problems by writing equations

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Examples “y” is the variable. Add 6 to each side to isolate the variable. Now divide both sides by 3. The answer is 5. Check the answer by substituting it into the original equation. 3y – 6 = 9 +6 +6 3y = 15 3 3 y = 5 3(5)-6=9 15 – 6 = 9 LT: I can solve equations and problems by writing equations

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Try this... Did you get x = - 4 ? You were right! LT: I can solve equations and problems by writing equations

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Solving Equations - let’s practice No sol. Identity or many solutions LT: I can solve equations and problems by writing equations

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Literal equations A literal equation is an equation that uses at least two different variables. You can solve literal equations for any of its one variables by using properties of equality. LT: I can solve equations and problems by writing equations

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Solving Literal Equations 1. Solve: V = πr 2 h, for h 2. Solve: de - 4f = 5g, for e LT: I can solve equations and problems by writing equations

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Homework P. 30 #11,13,17,19,23,26,27,29,31,37,39,47,55,57,62 Challenge# 65 LT: I can solve equations and problems by writing equations

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