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Warm ups

Warm ups. x + 11 = 29 5x + 16 = 51 n – ( -5 ) = 2 3 6 3. 3-3 Multi-Step Equations. Objective: To combine like terms and solve consecutive integers. To Clarify. Final answer MUST be in the form: letter = number

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Warm ups

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  1. Warm ups x + 11 = 29 5x + 16 = 51 n – (-5) = 2 3 6 3

  2. 3-3 Multi-Step Equations Objective: To combine like terms and solve consecutive integers.

  3. To Clarify . . . • Final answer MUST be in the form: • letter = number • You may NOT write a decimal answer unless there were decimals in the original problem. • Most answers will be either a whole number or a reduced, improper fraction • NO MIXED NUMBERS!!!

  4. Example 1 5x + 7 – 3x – 3 = 10 2x + 4 = 10 - 4 - 4 2x = 6 2 2 x = 3 Same side of the equation, combine like terms

  5. Check your Answer! • Always check answer in the original equation 5x + 7 – 3x – 3 = 10, x = 3 5(3) + 7 – 3(3) – 3 = 10 15 + 7 – 9 – 3 = 10 22 – 9 – 3 = 10 13 – 3 = 10 10 = 10 Use PEMDAS to simplify the left side

  6. TOO 1) x + x + 45 = 180 2) 4x – 3 – 6x = 15 3) 2x – x + 3 + 5 = 10 Answers: 1) x = 135/2 2) x = -9 3) x = 2

  7. Example 2 5x – 2(3 + x) = 12 5x – 6 – 2x = 12 3x – 6 = 12 + 6 + 6 3x = 18 3 3 x = 6 1st: Distribute 2nd: Combine like terms 3rd: Add/Subtract 4th: Multiply/Divide

  8. Check your Answer! • 5x – 2(3 + x) = 12, x = 6 5(6) – 2(3 + 6) = 12 5(6) – 2(9) = 12 30 – 18 = 12 12 = 12 No variables = No distributing!!

  9. WHAT ARE CONSECUTIVE INTEGERS? • Numbers in a row: • 1,2,3,4 • If I let x = 1, how could we represent “2” using “x”? • 2 = x + 1 • 3 = x + 2 • 4 = x + 3

  10. EXAMPLE 1 The sum of three consecutive integers is 105. Find the numbers. 1st: x 2nd: x + 1 3rd: x + 2 “sum” means add x = 34 x + 1 = 35 x + 2 = 36 x + x + 1 + x + 2 = 105 3x + 3 = 105 - 3 - 3 3x = 102 3 3 x = 34 Answer: 34, 35, 36

  11. MORE CONSECUTIVE INTEGERS Consecutive Integers Consecutive Even Integers Consecutive Odd Integers 1st: x 2nd: x + 2 3rd: x + 4 4th: x + 6 . . . 1st: x 2nd: x + 1 3rd: x + 2 4th: x + 3 . . . 1st: x 2nd: x + 2 3rd: x + 4 4th: x + 6 . . .

  12. EXAMPLE 2 The sum of four consecutive even integers is 116. Find the numbers. 1st: x 2nd: x + 2 3rd: x + 4 4th: x + 6 x = 26 x + 2 = 28 x + 4 = 30 x + 6 = 32 x + x + 2 + x + 4 + x + 6 = 116 4x + 12 = 116 - 12 - 12 4x = 104 4 4 x = 26 Answer: 26, 28, 30, 32

  13. TOO: WRITE AN EQUATION AND SOLVE with a partner Find three consecutive integers whose sum is -48. Find three consecutive odd integers whose sum is -27. **Watch your signs**

  14. Homework • 3-3 Practice Worksheet

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