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Unit 7: Two-Step Equations and Inequalities

Unit 7: Two-Step Equations and Inequalities. Lesson 1 – Two-Step Equations. Cornell Notes Header. Group Question. What is the difference between: 3 + 2(6) = x and 10x + 8 = 28

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Unit 7: Two-Step Equations and Inequalities

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  1. Unit 7: Two-Step Equations and Inequalities Lesson 1 – Two-Step Equations

  2. Cornell Notes Header

  3. Group Question • What is the difference between: 3 + 2(6) = x and 10x + 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.

  4. Order and Reverse Order of Operations • Order of Operations: Please Excuse My Dear Aunt Sally parentheses, exponents, multiplication & division, addition and subtraction ( ), x2, ∙ and ÷, + and – • Reverse Order of Operations: - and +, ÷ and ∙, x2, and ( )

  5. 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

  6. Solving Two-Step Equations - 8 - 8 5x = 35 ___ ___ 5 5 x = 7

  7. Solving Two-Step Equations Example • x/9 - 4 = 10 • x/9 - 4 = 10 + 4 + 4undo subtraction first by adding x/9= 14 9 · x/9= 14 · 9 undo the division by multiplying x = 126 check: 126/9 - 4 = 10 14 - 4 = 10 10 = 10

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

  9. 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 = 30 add the parentheses 2 ·(x+ 7)/2 = 30 · 2 undo division first by multiplying x + 7 = 60 - 7 - 7 undo the addition by subtracting x = 53 check: (53 + 7)/2 = 30

  10. 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.

  11. Working Backwards with Function Rules + 3 +3 4x = 36 __ __ 4 4 x = 9

  12. 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 = 40 - 16 -16 6x = 24 -------- 6 6 x = 4 races

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

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