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When simplifying mathematical expressions, it's crucial to perform operations in the correct sequence to get the right answer. This sequence is known as the order of operations. In algebra, we follow the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's apply this to the exercise provided. First, we evaluate the expression inside the parentheses, \( (-4)+7 \), which is the calculation we need to perform before moving on to other operations.

In the given exercise, after simplifying within the parentheses, the student correctly moved on to the addition step since there were no other operations left. This demonstrates the importance of understanding and following the order of operations in algebra.

The process of combining like terms involves simplifying algebraic expressions by adding or subtracting coefficients of terms that have the same variable and exponent. In the simple problem provided, this concept doesn't come into play because we are dealing with integers, not variable terms.

However, if the exercise included variable terms, the student would need to combine coefficients that have the same variable parts. For example, simplifying \(3x + 4x\) involves adding the coefficients of the 'x' terms together, resulting in \(7x\).

Understanding how to combine like terms is essential when working with more complex algebraic expressions, and it's a foundational skill that helps in solving equations and understanding the structure of algebraic expressions.

Adding integers is a fundamental operation in math. Integers include all whole numbers and their negative counterparts, including zero. There are some rules to consider when adding integers:

If both numbers are positive, you add their absolute values together. For two negative numbers, you also add their absolute values together, but the result is negative. When dealing with a positive and a negative number, like in our exercise \( (-4) + 7 \), the operation becomes more about finding the difference between their absolute values.

The sign of the result comes from the number with the larger absolute value, which is why in the initial step \( (-4) + 7 \) equals 3. This accurately applies the rule, as the larger number, 7 (positive), dictates the positive sign of the answer. The subsequent addition of positive integers \(9 + 3\) is straightforward, resulting in 12, which is the final solution to this part of the exercise.