Problem 82 - Elementary Algebra

Question

\(5-4 \cdot 3+8\)

Step-by-Step Solution

Answer

The solution to is simplifying 1.

Step 1: Apply the Order of Operations

Remember to use the order of operations, often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 2: Perform Multiplication

First, perform the multiplication operation in the expression: 4 \times 4 \times 3 = 1-2x = 4 3 = 1-+12\(.3 Therefore, the expression simplifies to 5 -12+8.12).= 5 -12+8\).= 5 -\(.-4:12\). 5 -12+8Therefore = 5 -12+8 5 -12+8 5 Therefore 5 ) This simplifies Therefore resulting 5 -12+8\( result 5 -12 Therefore fifth result Therefore\) remaining 8 5 -12+8.12\( calculation therefore. next 5 subtraction .remaining. 12+8\).minus then- Result:-4=Therefore. 12+$ non-nanol multiplication Therefore 5 -12+8.result .step multiplication remaining Remember..

Step 3: Perform Subtraction and Addition

Finally, perform the subtraction and then the addition from left to right: 5 - 12 = -7 Therefore, the simplified expression is -7 + 8 = 1. Therefore, the expression simplifies to 1.

Key Concepts

PEMDAS

To solve expressions like these, it's crucial to follow the order of operations, often abbreviated as PEMDAS. PEMDAS stands for:

• Parentheses first
• Exponents (i.e., powers and roots, etc.)
• Multiplication and Division (left-to-right)
• Addition and Subtraction (left-to-right)

Whenever you see a math problem, think PEMDAS. This will help you determine the correct sequence to solve the problem. In our example, we have the expression:

\(5-4 \cdot 3+8\)
Steps to follow:
1. Look for any parentheses (none here).
2. Look for any exponents (none here).
3. Perform any multiplications and divisions from left to right.
4. Perform additions and subtractions from left to right.

The expression becomes:

\(= 5-12+8\)

Basic Arithmetic

Basic arithmetic covers the fundamental operations: addition, subtraction, multiplication, and division. In this example, we use multiplication, subtraction, and addition.

Let's understand each operation involved:

• Multiplication: This operation combines groups of the same number. In our expression, it’s \(4 \cdot 3\).
• Subtraction: This decreases the value by subtracting one number from another. The expression \(5-12\).
• Addition: This increases the value by adding one number to another. The expression \(5-12+8\).

Knowing these operations helps us approach each step of simplifying the expression correctly.

Simplifying Expressions

Simplifying expressions involves breaking down a complex expression into a simpler form.
To simplify
\(5-4\cdot3+8\)
follow these steps:
1. **Multiplication**: Perform the multiplication operation first. So, calculate \(4\cdot3 = 12\).
2. **Rewrite the Expression**: Replace the multiplication result in the original expression. It now becomes \(5-12+8\).
3. **Subtraction**: Solve the subtraction \(5-12 = -7\).
4. **Addition**: Add the previous result to 8: \(-7+8 = 1\).

Therefore, the expression simplifies to 1. Remember, by carefully following each step and applying the order of operations, you can simplify any expression.