There are 4 consecutive odd integers that add up to –144. What is the greatest of the 4 integers?

Answer 1

Let the four consecutive odd integers be represented as \(x, x+2, x+4, x+6\). The sum of these integers can be expressed as:

\[ x + (x + 2) + (x + 4) + (x + 6) \]

We can simplify this sum:

\[ x + x + 2 + x + 4 + x + 6 = 4x + 12 \]

According to the problem, this sum equals -144:

\[ 4x + 12 = -144 \]

Next, we will solve for \(x\). Start by isolating \(4x\):

\[ 4x = -144 - 12 \] \[ 4x = -156 \]

Now divide both sides by 4:

\[ x = \frac{-156}{4} = -39 \]

Now, we can find the four consecutive odd integers:

1. The first integer: \(x = -39\)
2. The second integer: \(x + 2 = -39 + 2 = -37\)
3. The third integer: \(x + 4 = -39 + 4 = -35\)
4. The fourth integer: \(x + 6 = -39 + 6 = -33\)

Thus, the four consecutive odd integers are \(-39, -37, -35, -33\).

To find the greatest of these integers:

\[ \text{Greatest integer} = -33 \]

Finally, we confirm that their sum equals -144:

\[ -39 + (-37) + (-35) + (-33) = -144 \]

Therefore, the solution is verified, and the greatest of the four integers is:

\[ \boxed{-33} \]