Question

There are 4 consecutive odd integers that add up to –288. What is the value of the least integer?

Answer 1

Let the four consecutive odd integers be represented by:

\[
x, x + 2, x + 4, x + 6
\]

where \( x \) is the smallest integer. According to the problem, their sum is given as:

\[
x + (x + 2) + (x + 4) + (x + 6) = -288
\]

Now, we can combine like terms:

\[
4x + 12 = -288
\]

Next, we will isolate \( x \) by first subtracting 12 from both sides:

\[
4x = -288 - 12
\]
\[
4x = -300
\]

Now, divide both sides by 4 to solve for \( x \):

\[
x = -75
\]

Thus, the four consecutive odd integers are:

\[
-75, -73, -71, -69
\]

To find the value of the least integer, we simply take the value of \( x \):

\[
\text{Least integer} = -75
\]

Lastly, we can verify the sum to ensure correctness:

\[
-75 + (-73) + (-71) + (-69) = -75 - 73 - 71 - 69
\]
Calculating step by step:

\[
-75 - 73 = -148
\]
\[
-148 - 71 = -219
\]
\[
-219 - 69 = -288
\]

The calculation confirms that the total is indeed \(-288\).

Therefore, the value of the least integer is:

\[
\boxed{-75}
\]