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Mastering Multi-Step Equations and Consecutive Numbers: Lesson 7-2 Overview

This lesson focuses on solving multi-step equations and introduces the concept of consecutive numbers. We'll tackle examples such as 2x + 7 + 3x = 42, where we first combine like terms to simplify the equation. The lesson also covers setting up equations for word problems, including consecutive integers and their properties. By the end, you will learn how to find three consecutive numbers whose sum is a given value and address various types of number sequences. Engage with practice problems to solidify your understanding!

alexandra-valdez
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Mastering Multi-Step Equations and Consecutive Numbers: Lesson 7-2 Overview

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  1. 1-19-11 • Bellwork #38 • HW, red pen, book, pencil on desk.

  2. Solving Multi-step Equations Lesson 7-2 p.340

  3. Multi-step equations • Here is another type of equation that we can solve: • 2x + 7 + 3x = 42 • How is this equation different?

  4. Multi-step equations • Here is another type of equation that we can solve: • 2x + 7 + 3x = 42 • How is this equation different? • There are two x terms in the equation.

  5. Multi-step equations • To solve this type of equation, we first combine like terms, then solve as before. • 2x + 7 + 3x = 42 5x + 7 = 42

  6. Multi-step equations • To solve this type of equation, we first combine like terms, then solve as before. • 2x + 7 + 3x = 42 5x + 7 = 42 first combine like terms -7 -7subtract 7 from both sides 5x = 35 5 5 divide both sides by 5 and x = 7 solve.

  7. Try This • 4g + 6g -3 = 37 • -7y + 9 + 3y = 41

  8. Try This • 4g + 6g -3 = 37 g = 4 • -7y + 9 + 3y = 41

  9. Try This • 4g + 6g -3 = 37 g = 4 • -7y + 9 + 3y = 41 y = -8

  10. Word Problems • Some word problems can be set up as an equation and solved in the same way. A common type is the “consecutive integer” problem. • What does the word consecutive mean?

  11. Word Problems • Some word problems can be set up as an equation and solved in the same way. A common type is the “consecutive integer” problem. • What does the word consecutive mean? • It means “in sequence” or “in order”

  12. Word Problems • Some word problems can be set up as an equation and solved in the same way. A common type is the “consecutive integer” problem. • What does the word consecutive mean? • It means “in sequence” or “in order” • 13,14,15 are consecutive numbers. • So are -4, -3, -2.

  13. Consecutive numbers • Find 3 consecutive numbers whose sum is 48. • Let the smallest number = n. • The next number is one more than n so the next number = n + 1 • The third number is two more than n so the third number is n + 2

  14. Consecutive numbers • 1st number = n • 2nd number = n + 1 • 3rd number = n + 2 • The sum of the three numbers is 48, so n + n + 1 + n + 2 = 48 3n + 3 = 48 3n = 45 n = 15

  15. Consecutive numbers • 1st number = n n = 15 • 2nd number = n + 1 n + 1 = 16 • 3rd number = n + 2 n + 2 = 17 • The consecutive numbers are 15, 16, 17

  16. Try This • The sum of 3 consecutive numbers is 78. Find the three numbers.

  17. Try This • The sum of 3 consecutive numbers is 78. Find the three numbers. • 25, 26, 27

  18. More consecutive numbers • Sometimes a problem might ask for consecutive even numbers. An example would be 8,10,12. • What is the difference between the first 2 numbers?

  19. More consecutive numbers • Sometimes a problem might ask for consecutive even numbers. An example would be 8,10,12. • What is the difference between the first 2 numbers? +2 • What is the difference between the first and last number?

  20. More consecutive numbers • Sometimes a problem might ask for consecutive even numbers. An example would be 8,10,12. • What is the difference between the first 2 numbers? +2 • What is the difference between the first and last number? +4 • The three numbers are n, n+2, and n+4

  21. Let’s try one • Find 3 consecutive ODD integers whose sum is 105.

  22. Let’s try one • Find 3 consecutive ODD integers whose sum is 105. • 33, 35, 37

  23. Agenda 1-19-10 • PA#2 • P.343#4-6, 11-16, 27,28

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