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Lesson 1 – Two-Step Equations

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Cornell Notes Header Topic: Inequalities & Two-Step Equations (Unit 7 pg. 1) E. Q.: How are two-step equations applied in the real world? Name: _____________________________ Date: _____________________________ Class: _____________________________ Chp. 10 Lesson 3 (6 th grade my.hrw.com) – Two-Step Equations

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Group Question What is the difference between: 3 + 2(6) = x and10x + 8 = 28 In the first equation, the output is unknown. To find the output, you must simplify the left side of the equation using the order of operations. In the second equation, an input is unknown. To find the input, you must work backward and use the reverse order of operations.

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Order and Reverse Order of Operations Order of Operations: Please Excuse My Dear Aunt Sally parentheses, exponents, multiplication & division, addition and subtraction ( ), x 2, ∙ and ÷, + and – Reverse Order of Operations: - and +, ÷ and ∙, x 2, and ( )

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Introduction Problem Mrs. Clark spent forty-three dollars at the grocery store. Eight dollars was spent on vegetables and the rest of the money was spent on five pounds of ribs. How much were the ribs per pound? Write and solve a two step equation to represent the problem. 5x + 8 = 43

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Solving Two-Step Equations 2. Check by substituting the value of the variable into the equation to see if it makes a true statement. 5(7) + 8 = 4343 = 43 true 1. Undo operations using the reverse of the order of operations. 5x + 8 = 43 Undo the addition first and then undo the multiplication x = 35 ___ 5 5 x = 7

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Solving Two-Step Equations Example x / = undo subtraction first by adding x / 9 = 14 9 · x / 9 = 14 · 9undo the division by multiplying x = 126check: 126 / = = = 10

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Solving Two-Step Equations Example Solve: x+7 / 2 = 30

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Solving Two-Step Equations Example The fraction bar, or division bar, acts as a grouping symbol, like the parentheses. x+7 / 2 = 30 (x+ 7) / 2 = 30add the parentheses 2 · (x+ 7) / 2 = 30 · 2undo division first by multiplying x + 7 = undo the addition by subtracting x = 53check: (53 + 7) / 2 = 30

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Function Rules Word Problem The rule for a certain function is to multiply the input by 4 and subtract 3. Find the input value when the output is 33. In the problem we are given the rule and the output and have to find the input for the given output. In order to solve this, we need to work backwards.

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Working Backwards with Function Rules 4. Check answer by substituting the input value into the function rule (equation). 4(9) – 3 = 3336 – 3 = 33 or 33 = Solve. 4x – 3 = 33 Undo the subtraction and then undo the multiplication. 2. Substitute the given output into the equation. 4x – 3 = Write an equation for the given function rule. The rule for a certain function is to multiply the input by 4 and subtract 3. Find the input value when the output is 33. 4x – 3 = y or y = 4x x = 36 __ __ 4 4 x = 9

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Group Problem: Working Backwards with Function Rules Derrick has save $40 for go-cart racing. The cost of a racing license is $16, and the cost of each race is $6. How many races can Derrick afford? Cost of a race times # of races + cost of license = total cost 6x + 16 = x = x = 4 races

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Summary Summarize your notes in one to two sentences using the words two-step equations and reverse order of operations.

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