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Simplifying expressions in algebra is about making a math problem easier to understand and solve. It often involves performing various operations like addition, subtraction, multiplication, and division. In this problem, we're focused on simplifying the expression -105 - (-68).To simplify means to reduce the expression to its simplest form.

For example, in this expression, you need to deal with a double negative first, which we'll discuss in the next section, and then proceed with the final arithmetic calculation. Simplifying expressions also means following the correct order of operations, usually remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here, since there are no parentheses or exponents, we will focus on addition and subtraction.

Handling double negatives can be tricky but once you understand the concept, it becomes straightforward. When you see a double negative, remember that two negatives make a positive.

In the expression -105 - (-68), the double negative occurs in the term -(-68). This means you are subtracting a negative number. According to the rules of arithmetic, subtracting a negative number is the same as adding its positive counterpart. Therefore, -(-68) becomes +68.

This simplifies our original expression to -105 + 68, making it easier to handle the arithmetic calculations in the next step.

Adding and subtracting integers is a basic but crucial concept in elementary algebra. When working with integers, pay attention to their signs (positive or negative). In this case, after simplifying the double negative, we need to add -105 and 68.

Here's a simple method to handle this:

• If the signs are different (like in -105 + 68), subtract the smaller absolute value from the larger absolute value. In our case, 105 - 68 = 37.
• Then, give the result the sign of the number with the larger absolute value, which in this case is 105. Hence, the final result is -37.

This way, -105 + 68 simplifies to -37. Remember, the key is to keep track of the signs and perform each step carefully.