Problem 28 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 9+5(6-2) $$

Step-by-Step Solution

Answer

29

Step 1: Understand the Problem

The given expression is 9 + 5(6 - 2). Evaluate the expression inside the parentheses first.

Step 2: Solve Inside Parentheses

Calculate the value inside the parentheses: \(6 - 2\). \[6 - 2 = 4\]

Step 3: Multiply

Multiply the value obtained from inside the parentheses by 5: \[5 \times 4 = 20\]

Step 4: Addition

Add the results from the previous steps to the number 9: \[9 + 20 = 29\]

Key Concepts

Order of Operations

When solving algebraic expressions, it’s crucial to follow the correct sequence. This sequence is dictated by the Order of Operations, often remembered through the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Ignoring this order can lead to incorrect results. For example, in our given expression, we need to perform the operations inside the parentheses first before doing any multiplications or additions. Always follow PEMDAS to ensure accurate results.

Parentheses Evaluation

Parentheses are an integral part of many algebraic expressions and play a pivotal role in determining the order in which operations are performed.
By evaluating the content inside the parentheses first, you ensure that the most impactful calculations are done first, aligning with PEMDAS.
In our exercise, the expression is 9 + 5(6 - 2). We start by calculating the value inside the parentheses: \[6 - 2 = 4\]
This simplification helps us proceed confidently to the next operations.

Basic Multiplication

After evaluating the parentheses, multiplication usually comes next in the order of operations.
In our given problem: 9 + 5(6 - 2), once we simplified what's inside the parentheses to get 4, we move on to multiplication.
So, we multiply the number outside the parentheses by our result: \[ 5 \times 4 = 20 \]
Multiplication before addition ensures the expression is simplified correctly.

Basic Addition

Basic addition is one of the final steps when solving many algebraic expressions, especially after multiplication.
In our example, after we evaluate the parentheses and perform the multiplication, we add the results.
So, the expression turned from 9 + 5(6 - 2) to 9 + 20. Finally, we perform the addition: \[ 9 + 20 = 29 \]
Addition combines all the simplified values to find the final answer to the expression.