find 4 consecutive odd integers such that the sum of 7 times the smallest number and twice the largest is -91.

If first odd integer = n, then second = n + 2, third = n + 4, and fourth = n + 6.

7n + 2(n + 6) = -91

Solve for n.

Let's denote the first odd integer as "x".

Since the integers are consecutive odd numbers, the second odd integer would be x + 2, the third would be x + 4, and the fourth would be x + 6.

According to the given information, we can set up an equation:

7x + 2(x + 6) = -91

Now, let's solve this equation step by step:

Step 1: Distribute the 2 to x + 6:
7x + 2x + 12 = -91

Step 2: Combine like terms:
9x + 12 = -91

Step 3: Move the constant term to the other side of the equation by subtracting 12 from both sides:
9x = -103

Step 4: Divide both sides of the equation by 9 to isolate x:
x = -103/9

Step 5: Simplify the fraction:
x ≈ -11.44

Since x represents the smallest odd integer, we need to find the next consecutive odd integers by adding 2, 4, and 6 to x:

The four consecutive odd integers are approximately:
x ≈ -11.44
x + 2 ≈ -11.44 + 2 ≈ -9.44
x + 4 ≈ -11.44 + 4 ≈ -7.44
x + 6 ≈ -11.44 + 6 ≈ -5.44

To summarize, the four consecutive odd integers are approximately -11.44, -9.44, -7.44, and -5.44.

To find four consecutive odd integers, we can assign a variable to the smallest number and express the other three consecutive odd integers in terms of that variable.

Let's assume the smallest odd integer is represented by 'x'. The next three consecutive odd integers can be expressed as (x + 2), (x + 4), and (x + 6).

According to the given information, we need to find four consecutive odd integers in which the sum of 7 times the smallest number and twice the largest number is equal to -91.

To find these four consecutive odd integers and solve the equation, we can set up the following equation:

7x + 2(x + 6) = -91

Now, we can solve this equation to find the value of 'x' and subsequently determine the four consecutive odd integers.

7x + 2x + 12 = -91
9x = -103
x = -103/9

By dividing -103 by 9, we find that 'x' is approximately -11.44.

However, since we are dealing with integers, we need to find the nearest integer to -11.44. In this case, we round it down to -12.

Now, we can calculate the four consecutive odd integers:

First odd integer: x = -12
Second odd integer: x + 2 = -12 + 2 = -10
Third odd integer: x + 4 = -12 + 4 = -8
Fourth odd integer: x + 6 = -12 + 6 = -6

Therefore, the four consecutive odd integers that satisfy the given conditions are -12, -10, -8, and -6.