Question

The sum of 5 consecutive integers is –35. What is the greatest of these integers?

Answer 1

Let the five consecutive integers be represented as \(x, x+1, x+2, x+3, x+4\).

To find the sum of these integers, we can set up the equation:

\[
x + (x+1) + (x+2) + (x+3) + (x+4) = -35
\]

Simplifying the left side, we get:

\[
5x + (1 + 2 + 3 + 4) = -35
\]

\[
5x + 10 = -35
\]

To isolate \(5x\), we will subtract 10 from both sides:

\[
5x = -35 - 10
\]

\[
5x = -45
\]

Now, we divide both sides by 5:

\[
x = -9
\]

With \(x\) found, the five consecutive integers are:

\[
-9, -8, -7, -6, -5
\]

The greatest of these integers is:

\[
\boxed{-5}
\]

To verify, we can check the sum of these integers:

\[
-9 + (-8) + (-7) + (-6) + (-5) = -35
\]

Since the sum is indeed -35, the solution is confirmed. The greatest integer is

\[
\boxed{-5}
\]