Problem: Find the other integer when the sum of two integers is -12 and one of them is 43.

Solution:

To find the other integer, we can use the concept of algebraic equations. Let's assign variables to the two integers and create an equation based on the given information.

Let's assume the two integers are x and y. Given that the sum of the two integers is -12, we can write the equation as follows:
x + y = -12

We are also given that one of the integers is 43. Let's substitute this value into the equation:
43 + y = -12

Now, we can solve this equation to find the value of y.

Solving the equation:

To isolate y on one side of the equation, we will subtract 43 from both sides:
43 + y - 43 = -12 - 43
y = -55

Therefore, the other integer is -55.

Explanation:

1. Assign variables and create an equation:
- Let x represent one integer and y represent the other integer.
- Write the equation: x + y = -12.

2. Substitute the given value:
- Since one of the integers is 43, substitute x with 43 in the equation: 43 + y = -12.

3. Solve the equation:
- Subtract 43 from both sides of the equation: 43 + y - 43 = -12 - 43.
- Simplify the equation: y = -55.

4. Conclusion:
- The other integer is -55.

Summary:

The other integer is -55. By following the given steps, we assigned variables to the two integers, created an equation based on the given information, substituted the value of one integer into the equation, and solved the equation to find the value of the other integer.

-55