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 \(-24\).
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