The sum is 3*(x-1) or 3x - 3
72/3 = 24 and 7+8+9 = 24 so the integers are 7, 8 and 9.
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.
1+8+0 = 9 or 180+80+0 = 260
Algebraically. X = integer. X + (X + 1) + (X + 2) = - 123 3X + 3 = - 123 3X = - 126 X = - 42 X + 1 = - 41 X + 2 = - 40 - 42 + - 42 + - 40 = -123 =======
I'm assuming this is supposed to say: "What are three consecutive integers that add together to equal 171?"This could also be "What are three consecutive integers that multiply together to equal 171?"I will do both.For the addition caseThink of "three consecutive integers" as the expressions x, x+1, and x+2. For any value of x, these three expressions will give that number, the number that is one greater than it, and the number that is two greater than it. So, the expression x+(x+1)+(x+2) is the general sum of three consecutive integers. Also possible is the expression x+(x-1)+(x-2), which are still three consecutive integers. So, this is a simple equation:x+(x+1)+(x+2)=171x+x+1+x+2=1713x+3=1713x=168x=168/3x=56Since x=56, x+1=57 and x+2=58So the three numbers are 56,57,and 58You can check this answer by adding the three numbers together. I'll bet they equal 171.For the multiplication case:Refer to the explanation for the addition case, but instead of the end expression being x+(x+1)+(x+2), it is now the multiplication of the three integers, meaning the expression is (x)(x+1)(x+2), so we get: (x)(x+1)(x+2)=171(x)(x2+3x+2)=171x3+3x2+2x=171I'll admit right now I don't know a simple way to solve this equation, which hints to me that addition was the intent of the question, but this equation can be solved by plotting the equationsy=x3+3x2+2xy=171and finding their point(s) of intersection. The value comes out to be approximately 4.6106, which means that the numbers 4.6106, 5.6106, and 6.6106 will multiply to equal approximately 171 (but not exactly). No exact answer is really possible here.
The sum of three consecutive integers is -72
51
This would be impossible - since the mean of the three integers would have to be an integer, and if you divide -56 by 3, you do not get an integer.
11
There is no set of three consecutive odd or even integers whose sum is negative 31.
0.75*(2n+1) where n is an integer.
21, 22 and 23.
The integers are 53, 55 and 57.
-13, -15 and -17
They are 14, 16 and 18.
18
There are only 3 sets of consecutive even integers less than 12, you can work it out...