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Let the inegers be x+1, x+3, and x+5, these are 3 consecutive odds, we could have used x and x+1 and x+3, if x was odd Now the next part is often confusing. So let's say the sum was S, we have S=2(x+1)-5. Now, S= 3x+9 So we have 3x+9=2x+2-5 or x=-9-5+2 so x=-12 x+1=-11 which is odd x+3=-9 x+5=-7 The sum is -27 -27=2(-11)-5 So to see for usre if this works.. our sum is -27 and that is 5 less than twice -11 which is -22. That is to say -27 is 5 less than -22. Would this work with the positive integers 7, 9, and 11? The sum is 27 and the smallest is 7, but 27 does not equal 14-5, so no.

Q: The sum of three consecutive odd integers is 5 less than twice the smallest of these integers?

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This equation works out to 2x = x + 11. This is because the three consecutive odd integers can be represented by x, x + 2, and x + 4. From the equation 2x - x = 11, so x = 11. Checking, 2 times 11 = 22 which is 7 more than 15. The three integers are 11, 13 and 15.

98

The numbers are 14, 16 and 18.

The three integers, since they are consecutive, can be listed as a, a+1, and a+2. Twice the first is 2a. Three times the third is 3(a+2) = 3a+6. First make a formula of the information given: 2a+(3a+6)= -24 Next, solve the formula: 5a + 6 = -24 Subtract 6 from each side. 5a = -30 Divide each side by 5. a = -6 The three consecutive numbers are -6, -5, and -4.

Since we know that the integers are even and consecutive, we can call them x, x+2, x+4, and x+6, with x being the smallest of the four. twice the sum of the second and third can be written as 2(x+2+x+4)=4x+12 the sum of the first and fourth increased by 14 is x+x+6+14=2x+20 Then we can solve 4x+12=2x+20-->2x=8-->x=4 4

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three consecutives numbers: a = smallest a+2 a+4 14 less = -14 than twice the smallest = 2a so... a+a+2+a+4=-14+2a 3a+6=-14+2a 3a-2a=-14-6 a=-20 answer: smallest = -20 greatest = -16

-- Call the three consecutive integers (x-1), x, and (x+1).-- Twice the smallest is 2(x-1) or (2x-2).-- 12 more than the largest is (x+1)+12 or (x+13).-- These are equal, so2x - 2 = x + 13Subtract 'x' from each side of the equation:x - 2 = 13Add 2 to each side:x = 15 .-- The smallest of the three numbers is (x-1) = 14.-- The three consecutive integers are 14, 15, and 16.-- Twice the smallest is 28.-- 28 is 12 more than 16.QED, man, QED !

7, 8, 9 Let x be the smallest of the three integers; thus, the integers are x, x+1, x+2. From the problem, we get: 2x=(x+2)+5=x+7 2x-x=7 x=7

They are (14, 15, 16).

Suppose the smallest integer is A. The next two even numbers are A+2 and A+4. Using the information supplied we can form an equation: 2A - 14 = A + A+2 + A+4 Rearranging: 2A - 14 = 3A + 6 -20 = A So the three integers are -20, -18 and -16.

This equation works out to 2x = x + 11. This is because the three consecutive odd integers can be represented by x, x + 2, and x + 4. From the equation 2x - x = 11, so x = 11. Checking, 2 times 11 = 22 which is 7 more than 15. The three integers are 11, 13 and 15.

98

Let the smallest integer be x. Since the consecutive even integers differ by 2, we havex + 2(x + 2) = (x + 4) + 203x + 4 = x + 24 (subtract x and 4 from both sides)3x - x - 4 + 4 = x - x - 4 + 242x = 20 (divide by 2 to both sides)x = 10Thus, the three consecutive even integers are 10, 12, and 14.

18, 20 and 22

They are 14, 16 and 18.

Integers are n, n + 1 and n + 2, so 3n + 3 = 13 + 2n Subtract 2n from each side: n + 3 = 13 Subtract 3 from each side: n = 10 Job done.