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When adding integers, it is helpful to visualize the number line. Integers include both positive and negative numbers. For example, in the expression \(6 + (-12) + 8\), we first look at the addition of 6 and -12. We can think of this as starting at 6 on the number line, then moving 12 units to the left (because -12 is negative). This results in -6.Understanding how to move along the number line makes adding positive and negative numbers easier. Always pay attention to the signs. If the signs are the same, you add the numbers and keep the sign. If the signs are different, you subtract the smaller number from the larger one and take the sign of the larger number.

Let's break this into a simpler process:

• Identify the integers and their signs.
• If the signs are the same, add them.
• If the signs are different, subtract the smaller number from the larger one.
• Finally, take the sign of the larger number.

Combining like terms means to simplify expressions by merging terms that have the same variables to a single term. However, in this exercise, the terms are just constant integers. In such cases, the goal is to simplify the expression by combining these constants into a single integer.

Here, the terms are 6, -12, and 8. To simplify,

• First, add 6 and -12.
• Then, add the result to 8.

Using this method, we first calculate \(6 + (-12)\). This is equivalent to subtraction: 6 - 12, which equals -6. Next, we add -6 and 8. Again, because the signs are different, we subtract 6 from 8, resulting in 2.With practice, combining like terms becomes intuitive, and understanding this fundamental skill is key in algebra.

Negative numbers are simply numbers less than zero, often visualized on a number line to the left of zero. In arithmetic, dealing with negative numbers carefully is essential.

To add negative numbers to positive numbers, follow these steps:

• Start with the positive number.
• Move left on the number line by the absolute value of the negative number.

To handle our example \(6 + (-12) + 8\), starting from 6, we move 12 steps to the left (negative direction), landing on -6. From -6, we move 8 steps right (positive direction), landing on 2.
Negative numbers need attention to their signs, especially when combined with positive numbers. Misinterpreting these can lead to errors, so always double-check each step to ensure accuracy.