the sum of 4 consecutive integers is -106

Let the four consecutive integers be represented as \( x \), \( x+1 \), \( x+2 \), and \( x+3 \).

The sum of these integers is given by:

\[
x + (x+1) + (x+2) + (x+3) = -106
\]

Simplifying the left-hand side:

\[
4x + 6 = -106
\]

Now, subtract 6 from both sides:

\[
4x = -106 - 6
\]
\[
4x = -112
\]

Next, divide both sides by 4:

\[
x = \frac{-112}{4} = -28
\]

So, the first integer is \( x = -28 \).

The four consecutive integers are:

\[
-28, -27, -26, -25
\]

Finally, we can check the sum:

\[
-28 + (-27) + (-26) + (-25) = -106
\]

Thus, the solution is correct.

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. What is the sum of 5 consecutive integers if the middle one is -10?
2. How do you express the sum of any \( n \) consecutive integers algebraically?
3. What is the sum of the first 20 consecutive positive integers?
4. Can the sum of 3 consecutive integers be a positive even number?
5. What is the sum of 4 consecutive odd integers?

**Tip:** The sum of consecutive integers can be quickly computed using basic algebra, as the numbers follow a predictable linear pattern.

The sum of 4 consecutive integers is -106.

Learn how to solve the problem where the sum of 4 consecutive integers is -106. This problem uses algebraic techniques and linear equations, providing a step-by-step solution suitable for students in Grades 6-8.

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