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**Lesson 3.4- Solving Multi-Step Equations, pg. 142**

Objectives: To solve problems by working backward. To solve equations involving more than one operation.

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Vocabulary Multi-Step Equations: equations with more than one operation. Consecutive Integers: integers in counting order. Consecutive integers: 7, 8, 9,… Consecutive odd integers: 5, 7, 9, 11.. Consecutive even integers: 10, 12, 14, 16… Number theory: the study of numbers and the relationships between them.

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**Ex. 1: Solve each problem by working backwards.**

A number multiplied by seven, and then the product is added to 13. The result is 55. What is the number? The English alphabet contains 2 more than twice as many letters as the Hawaiian alphabet. How many letters are there in the Hawaiian alphabet?

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3. Nine is subtracted from a number, and then the difference is multiplied by 5. The result is 75. What is the number?

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**Steps for Solving Multi-Step Equations**

Step 1: Undo addition and subtraction Step 2: Undo multiplication and division. Step 3: Check

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**Ex. 2: Solve each equation.**

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3. n + 3 = 8.6

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y – 1.5 = 5.32 = 5p + 3

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**Ex. 3: Write an equation and solve each problem.**

Twelve decreased by twice a number equals Find the number.

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**2. Find three consecutive integers whose sum is 42.**

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**3. Find three consecutive even integers whose sum is -30.**

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**Summary Steps for Solving Multi-Step Equations**

Step 1: Undo addition or subtraction. Step 2: Undo multiplication or division. Step 3: Check. Consecutive integers: n, n+1, n+2,… Consecutive odd integers: n, n+2, n+4,… Consecutive even integers: n, n+2, n+4,… NBA #18, pg. 146, problems even

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