Problem 26 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ -4-(-6) $$

Step-by-Step Solution

Answer

2

Step 1 - Understand the Problem

The exercise requires evaluating the expression $$-4 - (-6)$$.

Step 2 - Simplify the Double Negative

Notice the double negative in the expression. Subtracting a negative number is the same as adding its positive counterpart: $$-4 - (-6) = -4 + 6.$$

Step 3 - Calculate the Result

Now, add the numbers: $$-4 + 6 = 2.$$

Key Concepts

Double Negative

In algebra, encountering a double negative in an expression can be puzzling at first. However, understanding the double negative is crucial for simplifying expressions correctly. When you see two negative signs, as in $$-(-6)$$, it means you are subtracting a negative number. Subtracting a negative number is the same as adding its positive counterpart. For instance, $$-(-6)$$ becomes $$+6$$. This is because subtracting something negative is like taking away a debt; effectively, you are gaining or adding more.

Simplifying Expressions

Simplifying an expression means reducing it to its simplest form. This includes combining like terms and removing unnecessary brackets. Take the expression $$-4 - (-6)$$ from our example. First, address the double negative to obtain $$-4 + 6$$. Now, the expression is simpler and easier to evaluate. By simplifying expressions, the arithmetic becomes straightforward, and we can focus on performing basic operations to find the final result.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. Let's focus on addition and subtraction, which are key to solving our expression. Once we simplified $$-4 - (-6)$$ to $$-4 + 6$$, the next step is to perform the addition. Adding a positive number to a negative number involves moving to the right on the number line. Here, $$-4 + 6$$ means starting at -4 and moving 6 units to the right, which lands us at 2. Thus, mastering these basic operations makes solving algebraic expressions much more manageable.

Number Line

A number line is a visual representation of numbers in a straight horizontal line. It helps in understanding and performing arithmetic operations like addition and subtraction, especially with negatives. Imagine our expression, $$-4 + 6$$, on a number line. Start at -4. Each positive step (+1) takes you one unit to the right. Counting six steps to the right from -4 takes you to 2. Using the number line makes it easier to visualize the arithmetic and understand concepts like adding and subtracting negative numbers.