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2.3 Solving Multi-Step Equations: Combining like Terms: Simplify the terms with the same variable using arithmetic. Term: A number, a variable or a product or quotient of numbers and variables that is added or subtracted in an algebraic expression.

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GOAL:

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We solve multi-step equations by forming a series of simpler equations by first using combination of like terms: Ex: What is the solution of 5 = 5m – m 5 = 5m – m 5 = 5m + 2m – 23 5 = 7m – 23 Add like terms Inverse of subtraction 28 = 7m __ ___ 7 7 Inverse of multiplication m = 4 Dont forget to check!! Same variable

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REAL-WORLD: A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket for $19 per ticket. The web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?

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SOLUTION: Using the given info we have: Each ticket (x) costs $ x One time charge of $ The family paid = $1132 Insurance for each ticket is $19 19x 167x + 19x + 16 = 1132

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186x + 16 = 1132 Like terms 186x = Inverse of Add 186x = 1116Like terms 186x /186 = 1116 /186 Inverse of mult. x = 6 Tickets

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YOU TRY IT: What is the solution of 11x – 8 – 6x = 22

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Solution: 11x – 8 – 6x = 22 11x – 6x – 8 = 22 5x – 8 = 22 Add like terms + 8 = +8 Inverse of subtraction 5x = 30 __ ___ 5 5 Inverse of multiplication x = 6Dont forget to check!! Same variable Given

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Solving equations with Distributive Property: Ex: What is the solution of – 8 (2x -1)= 36 – 8 (2x -1)= 36 – 8(2x) – 8(-1)= 36 – 16x + 8 = 36 Multiplication – 8 – 8 Inverse of addition _____ ____ – 16 – 16 Inverse of multiplication x = - 28/16 - 7/4 Dont forget to check!! Distributive – 8 – 16x = 28

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YOU TRY IT: What is the solution of 18 = 3(2x – 6 )?

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Solution: 18 = 3(2x – 6) 18 = 3(2x) + 3(-6) Multiplication Inverse of subtraction __ ___ 6 6 Inverse of multiplication x = 6 Dont forget to check!! Distributive 3 36 = 6x 18 = 6x – 18 Given

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Solving equations with fractions: Multiplication Same Denominator Common Denominator Subtraction

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Inverse of Multiplication Inverse of division ___ ___ 5 5 Dont forget to check!!

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YOU TRY IT:

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Solution: Add the numerators Common Denominator Opposite of dividing by 20

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Solution: 23b = 60Opposite of multiplying by 23 Dont forget to Check! Multiply by 20 both sides

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We never divide fractions, We keep, change and flip! Plug in our answer

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24 45 Cross Cancel: Divide a numerator with a denominator (only on the same fraction) Add the numerators: since our denominators are the same. Since 69/23 = 3 and 3 =3 we have gotten the right answer.

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VIDEOS: Multi-Step Equations Multi-Step nal-expressions/solving-rational-equations/v/ex-1- multi-step-equation g-linear-equations-and- inequalities/complicated_equations/v/ex-2-multi- step-equation

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Class Work: Pages: Problems: As many as you need to master the concepts.

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