Final answer:
To solve the problem, each set of parentheses is simplified first, then the resulting numbers are added together, taking care to change subtraction of a negative number to addition. The final answer to the expression (3+2-5)+2-(5-2-6) is 5.
Step-by-step explanation:
The student is asking how to perform operations with integers which involve addition and subtraction, including how to handle positive and negative numbers. Here is a step-by-step solution to the problem:
First, solve the innermost parentheses: (3+2-5). These are all positive numbers, so we simply add and subtract in order: 3+2 equals 5, then subtract 5, resulting in 0. So, the first part simplifies to (0).
Next, look at the second set of parentheses: (5-2-6). Again, we subtract in order: 5-2 equals 3, and then subtracting 6 from 3 gives us -3. So, this part simplifies to (-3).
Now, we can rewrite the original problem without parentheses: 0 + 2 - (-3). When we subtract negative numbers, we change the subtraction to addition and invert the sign of the number being subtracted. Therefore, -(-3) becomes +3.
So the operation now becomes 0 + 2 + 3. We can then add the numbers in any order because addition is commutative. Adding 2 and 3 gives us 5. Since the first number is 0, adding 0 to 5 does not change the value, and so our final answer is 5.