The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
n + n + 1 = –49; n = –25; n + 1 = –24
To solve this problem, we can use algebra and create an equation based on the given information. Let's assume the first integer is represented by 'x'.
Since we are considering consecutive integers, the second integer would be 'x + 1'.
According to the problem, the sum of these two integers is -49. We can express this information as an equation:
x + (x + 1) = -49
Now, let's solve the equation to find the values of the two integers:
2x + 1 = -49 [Combine like terms]
2x = -49 - 1 [Subtract 1 from both sides]
2x = -50 [Simplify]
x = -50/2 [Divide by 2 on both sides]
x = -25
So, the first integer is -25. To find the second integer, we can substitute the value of 'x' back into our equation:
-25 + 1 = -24
Therefore, the consecutive integers are -25 and -24.
x + x + 1 = -49
2x = -50
x = -25