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In mathematics, addition and subtraction are fundamental operations that help us solve equations and expressions. Addition is when we combine two or more numbers to get a sum.
Subtraction, on the other hand, is when we take away one number from another to get a difference.
In the given exercise, we are dealing with a combination of these operations. Let’s break it down for better understanding. When you see an addition of a negative number, like in the expression \(34 + (-19)\), it’s essentially a subtraction. This is because adding a negative number decreases the value.
Thus, \34 + (-19)\ can be rewritten as \34 - 19\, simplifying our task.

Integer operations include addition, subtraction, multiplication, and division of whole numbers. These operations follow specific rules:
- Adding two positive integers results in a positive sum.
- Adding two negative integers results in a negative sum.
- Adding a positive integer and a negative integer is like subtracting the absolute values and taking the sign of the larger absolute value. For instance, in the expression \(34 + (-19)\), we subtract 19 from 34 because they have opposite signs. The absolute value of 34 is greater, and since 34 is positive, the result is positive. Thus, \34 - 19 = 15\.

Algebraic simplification helps make expressions easier to work with. By reducing expressions to their simplest form, we make calculations quicker and more straightforward. In the exercise provided, simplification involved understanding and converting addition of a negative number into subtraction. First, recognize the operations involved. If an expression contains \(a + (-b)\), understand it as \a - b\.
This step alone simplifies the expression significantly. Next, perform the basic arithmetic to arrive at the final answer. In our example, \34 - 19\ results in the simplified form of 15. This process illustrates how recognizing and applying basic simplification rules can efficiently reduce complexity in algebra.