Problem 84 - Elementary Algebra

Question

\(-21-(4-9)\)

Step-by-Step Solution

Answer

-16

Step 1: Simplify the Expression Inside the Parentheses

First, solve the expression inside the parentheses. Subtract 9 from 4: (4 - 9) = -5

Step 2: Substitute the Simplified Value

Replace the parentheses with the simplified value. The problem becomes: -21 - (-5)

Step 3: Simplify the Subtraction of Negatives

Subtracting a negative number is the same as adding its positive counterpart: -21 - (-5) = -21 + 5

Step 4: Perform the Addition

Add the values: -21 + 5 = -16

Key Concepts

Parentheses in Algebra

Parentheses play a crucial role in algebra. They indicate which operations should be performed first. In the given exercise, we start by solving the expression inside the parentheses: \(4 - 9\). Think of parentheses as grouping symbols that tell you what to focus on first.

Here’s why they are important:

• They clarify the order of operations
• They help in breaking down complex expressions
• They prevent confusion and mistakes

Subtracting Negative Numbers

Subtracting negative numbers can be confusing at first. However, it’s important to remember that subtracting a negative is the same as adding the positive version of that number.

In the example, we have to simplify \(-21 - (-5)\). According to the rule, this becomes:\br \(-21 + 5\).

To make it simple:

• If you see \(-(-number)\), change it to \(+(number)\).
• This changes a subtraction problem into an addition one.

This rule makes working with negatives a bit easier.

Basic Algebraic Operations

Basic algebraic operations include addition, subtraction, multiplication, and division. In algebra, these operations often involve variables and constants. It’s essential to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In our exercise, the order of operations is:

• Solve inside the parentheses: \(4 - 9\), which equals \(-5\).
• Replace the simplified value: \(-21 - (-5)\).
• Subtract the negative (change to addition): \(-21 + 5\).

Understanding these basic operations helps in tackling more complex algebra problems.

Integer Addition and Subtraction

Adding and subtracting integers is a fundamental math skill. When dealing with both positive and negative integers, it’s crucial to keep the rules straight:

For addition:

• When both integers are positive, simply add them.
• When both integers are negative, add their absolute values and keep the negative sign.
• When one integer is positive and the other is negative, subtract the smaller absolute value from the larger absolute value and keep the sign of the integer with the larger absolute value.

For subtraction:

• Convert the problem into an addition problem by changing the subtraction sign to an addition sign and flipping the sign of the integer that follows.
• Then apply the rules of addition mentioned above.

In our example, after simplifying \(-21 - (-5)\) to \(-21 + 5\), you perform the addition and get \(-16\). Practicing these rules makes integer operations straightforward.