Question

The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers

Answer 1

Let the first integer be \( x \). Since the integers are consecutive, the next integer will be \( x + 1 \).

According to the problem, the sum of these two integers is \(-49\). Therefore, we can write the equation:

\[
x + (x + 1) = -49
\]

Simplifying the left side, we have:

\[
2x + 1 = -49
\]

Next, we will isolate \( x \) by subtracting 1 from both sides:

\[
2x = -49 - 1
\]
\[
2x = -50
\]

Now, divide both sides by 2:

\[
x = -25
\]

Now that we have the value of the first integer, we can find the second integer:

\[
x + 1 = -25 + 1 = -24
\]

Thus, the two consecutive integers are:

\[
-25 \quad \text{and} \quad -24
\]

In conclusion, the two consecutive integers are \(-25\) and \(-24\).