Final answer:
To solve for four consecutive integers where the sum of the second and fourth is -24, you set up an equation with x representing the first integer. The solution reveals that the four integers are -14, -13, -12, and -11.
Step-by-step explanation:
To solve the problem of finding four consecutive integers such that the sum of the second and fourth is -24, let's define the first integer as x. Therefore, the following integers will be x+1, x+2, and x+3. We are given that the sum of the second and fourth integer is -24, thus the equation will be:
(x+1) + (x+3) = -24
Combining like terms, we get:
2x + 4 = -24
Subtracting 4 from both sides:
2x = -28
Dividing both sides by 2:
x = -14
The consecutive integers are therefore -14, -13, -12, and -11. Checking our work: -13 + -11 equals -24, which satisfies the condition given in the problem.