The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
x = 1st odd integer
x + 2 = 2nd odd integer
x + 4 = 3rd odd integer
x + 6 = 4th odd integer
x + x + 2 + x + 4 + x + 6 = -104
4x + 12 = -104
4x = -116
x = -29
-29, -27, -25, -23
das
Let's solve this step-by-step.
Step 1: Let's assume the first odd integer as "x".
Step 2: The next odd integer will be "x + 2" because consecutive odd integers have a difference of 2.
Step 3: The third odd integer will be "x + 4" since we have added 2 to the second integer.
Step 4: The fourth odd integer will be "x + 6" because we are adding 2 again.
Step 5: The sum of these four consecutive odd integers is given as -104. So, we can set up the equation:
x + (x + 2) + (x + 4) + (x + 6) = -104
Step 6: Simplify the equation:
4x + 12 = -104
Step 7: Subtract 12 from both sides of the equation:
4x = -116
Step 8: Divide both sides of the equation by 4:
x = -29
Step 9: Now, substitute the value of x back into the equations we set up in Steps 2, 3, and 4 to find the other three odd integers:
x + 2 = -29 + 2 = -27
x + 4 = -29 + 4 = -25
x + 6 = -29 + 6 = -23
So, the four consecutive odd integers are -29, -27, -25, and -23.
To find the four consecutive odd integers, we will use the given information that their sum is -104. Let's assign x as the lowest odd integer in the sequence.
The next odd integer will be x + 2, since consecutive odd integers increase by 2.
The third odd integer will be x + 4, and the fourth odd integer will be x + 6.
Now we can set up the equation: x + (x + 2) + (x + 4) + (x + 6) = -104.
Combining like terms, the equation becomes:
4x + 12 = -104
Subtracting 12 from both sides of the equation:
4x = -116
Dividing both sides of the equation by 4:
x = -29
Therefore, the four consecutive odd integers are:
-29, -27, -25, -23.