Problem 28 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ -6-8 $$

Step-by-Step Solution

Answer

Answer: -14

Step 1: (Step 1: Identify the given numbers)

(We are given two numbers: -6 and -8. The operation that needs to be performed is subtraction.)

Step 2: (Step 2: Perform the subtraction operation)

(To subtract the numbers, we follow the rule for subtracting negative numbers. We change the sign of the second number and add it to the first number. In this case, we change the sign of 8 to -8 and add it to -6: $$-6 - 8 = -6 + (-8)$$)

Step 3: (Step 3: Add the numbers)

(Now we add the two numbers: $$-6 + (-8) = -14$$)

Step 4: (Step 4: Write down the final result)

(The result of the subtraction operation is $$-14$$. Therefore, $$-6 - 8 = -14$$.

Key Concepts

Subtraction of Integers

Subtraction of integers can be a bit tricky, especially when negative numbers are involved. The basic concept is to subtract one number from another, but when dealing with negative integers, we simply need to follow a special rule.

When subtracting integers, particularly with negative numbers, we invert the sign of the second number and change the operation to addition. For example, in the expression \(-6 - 8\), we change it to \(-6 + (-8)\).

This makes it easier because adding negative numbers follows straightforward rules.

Negative Numbers

Negative numbers are numbers less than zero. They represent opposites of positive numbers and are crucial in everyday calculations, such as temperature or elevations below sea level.

When working with negative numbers, keep in mind:

• The further left the number is on the number line, the smaller its value.
• Performing operations with negatives can sometimes lead to confusion, but breaking it down helps.

For instance, in our exercise, both numbers are negative, making the result even more negative after addition.

Rules of Addition and Subtraction

Understanding the rules of addition and subtraction with integers is essential. These rules help simplify calculations and reduce errors.

Here are key rules to remember:

• When adding numbers with the same signs, keep the sign and add the absolute values.
• When subtracting, change the sign of the second number and proceed with addition.

In the example \(-6 - 8\), changing it to \(-6 + (-8)\) led us to \(-14\), as both numbers were negative, confirming that negative stays negative and sum grows numerically.