1. find four consecutive even integers such that the sum of the first and third is 6 less than the largest 2. find four consecutive odd integers such that the largest equals 2 more than the sum of the other three 3. find two consecutive even integers such that twice the smaller is 26 less than three times the larger 4. find the consecutive integers such that twice the sum of the first and second is 27 more than three times the third 5. what are three consecutive integers such that three times the smallest added to 7 is 13 less than four times the largest 6. if three times the first of three consecutive integers is subtracted from twice the second the result is 16 more than the third. find the integers 7. find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742 8. when the smallest of three consecutive odd integers is added to four times the largest it produces a result 729 more than four times the middle integer. find the numbers 9. three consecutive multiples of 5 have a sum of 75 what are the numbers i'm sorry these are a lot but i need asap

An integer number is a Whole number which must not have any decimal. For example -5, -4, -3 -2, -1, 0, 1 2, 3, 4, 5. So an integer can be negative and positive.

Following are the formulas for calculating Even and Odd integers:

Let the even number be = X

consecutive even integers =  X, X + 2, X + 4, X + 6...etc

Odd number integer will be = 2X + 1

Consecutive Odd Integer numbers = (2X+ 1), (2X + 1+ 2), (2X+ 1+2+2)and so on.

Now the answers:

Four consecutive even integers such that the sum of the first and third is 6 less than the largest : Answer is -4, -2, 0, 2

Equation X + X + 2 = (X + 6) - 6

four consecutive odd integers such that the largest equals 2 more than the sum of the other three:  Answer -1, 1, 3, 5

Equation 2X+7 = (2X+1) + (2X+3) + (2X+5) + 2

Two consecutive even integers such that twice the smaller is 26 less than three times the larger: Answer 20, 22

The consecutive integers such that twice the sum of the first and second is 27 more than three times the Third: Answer 31, 32, 33

Three consecutive integers such that three times the smallest added to 7 is 13 less than four times the largest: Answer 12, 13, 14

Three times the first of three consecutive integers is subtracted from twice the second the result is 16 more than the third the integers: Answer 8, 9, 10

Four cons ecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742: Answer 120, 122, 124, 126

The smallest of three consecutive odd integers is added to four times the largest IT produces a result 729 more than four times the middle integer. find the numbers: Answer 721, 723, 727

Three consecutive multiples of 5 have a sum of 75 what are the numbers: Answer 20, 25, 30

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1. Let the first integer be represented by: 2k

the second integer by: 2(k+1)

the third integer by: 2(k+2)

and the fourth by: 2(k+3)

Then, 2k + 2(k+2) = 2(k+3) - 6

2k + 2k + 4 = 2k + 6 - 6

4k + 4 = 2k

4 = -2k

-2 = k

-4, -2, 0, 2

2. Let the first integer be represented by: 2k+1

the second integer by: 2k+3

the third integer by: 2k+5

and the fourth by: 2k+7

Then, 2k+7 = (2k+1) + (2k+3) + (2k+5) + 2

2k + 7 = 6k + 11

-4 = 4k

-1 = k

-1, 1, 3, 5

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step-by-step explanation: