Let's solve for the middle integer step by step.

We can represent the three consecutive integers as:

• The first integer: $x - 1$
• The middle integer: $x$
• The third integer: $x + 1$

According to the problem, the sum of these three integers is $-51$. Therefore, we can write the equation:

$(x - 1) + x + (x + 1) = -51$

Simplify the equation by combining like terms:

$x - 1 + x + x + 1 = -51$

$3x = -51$

Now, divide both sides by 3 to solve for $x$:

$x = \frac{-51}{3} = -17$

So, the value of the middle integer is $-17$.

Final Answer:

• Middle Integer: $-17$

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. The sum of four consecutive integers is 10. What is the value of the second integer?
2. What is the middle integer of three consecutive integers if their sum is 18?
3. If the sum of five consecutive integers is 15, what is the third integer?
4. Find three consecutive even integers whose sum is 72.
5. The sum of three consecutive odd integers is 33. What is the middle integer?

Tip: When dealing with consecutive integer problems, using a variable to represent the middle number can simplify the process of solving the equation.