Problem 73 - Elementary Algebra

Question

Simplify. $$ 5-2+2-1 $$

Step-by-Step Solution

Answer

The simplified result is 4.

Step 1: Identify Operations

We begin the simplification process by identifying the order of the operations involved in the expression: 5 - 2 + 2 - 1. This expression requires subtraction and addition. As there are no parentheses or multiplication/division involved, we'll solve from left to right.

Step 2: Perform First Subtraction

Start by performing the first subtraction operation in the sequence. Calculate \(5 - 2 = 3\).

Step 3: Perform Addition

Next, perform the addition with the result from step 2. Calculate \(3 + 2 = 5\).

Step 4: Perform Final Subtraction

Finally, perform the last subtraction using the result from step 3. Calculate \(5 - 1 = 4\).

Key Concepts

Understanding the Order of Operations

When tackling problems involving multiple operations, it's crucial to follow the **order of operations**. In mathematics, this order dictates how complex expressions are simplified correctly. For the expression \( 5 - 2 + 2 - 1 \), the operations are subtraction and addition.
Typically, the rule to follow is known as PEMDAS:

• P: Parentheses
• E: Exponents
• M/D: Multiplication and Division (from left to right)
• A/S: Addition and Subtraction (from left to right)

In our exercise, since only addition and subtraction are involved, we simplify them by working left to right in the expression. Paying close attention to this order helps in preventing mistakes and ensures getting the correct result.

Addition and Subtraction in Sequence

After establishing the correct order in which operations should be performed, the focus shifts to **adding and subtracting** numbers sequentially. In the expression \( 5 - 2 + 2 - 1 \), both addition and subtraction play a key role.
To solve:
1. **Subtraction**: Begin with the calculation from the start, as subtraction appears first in \(5 - 2\), yielding 3.
2. **Addition**: Once subtraction is completed, proceed to the next operation, addition in \(3 + 2\), resulting in 5.
3. **Final Subtraction**: Lastly, apply the final subtraction \(5 - 1\), which results in 4.
This step-by-step approach simplifies the process and assures accuracy in calculations. By addressing one operation at a time, one can clearly track each step and result without confusion.

Mastering the Simplification Process

The **simplification process** is essential for handling and reducing expressions to a single, final value. This involves carefully executing each mathematical operation in a systematic manner. In the given problem, simplifying \( 5 - 2 + 2 - 1 \), involves:

• Identifying operations to compute first based on the order (left to right since only addition and subtraction are present).
• Performing each operation one by one—begin with subtraction, follow with addition, and finish with a final subtraction.
• Tracking results at each step ensures the process remains clear and any interim calculations are accurate.

By adhering to these guidelines, the simplification process becomes straightforward and efficient. Understanding each stage and focusing on one calculation at a time makes algebraic problems less daunting and much more manageable.