Problem 27 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 8+6(5-3) $$

Step-by-Step Solution

Answer

The answer is 20.

Step 1: Evaluate the Expression Inside the Parentheses

Start by solving the expression inside the parentheses: \(5 - 3\).

Step 2: Simplify the Parentheses

Calculate \(5 - 3\) to get 2. Now the expression looks like this: \(8 + 6(2)\).

Step 3: Multiply

Next, multiply 6 by 2. So, \(6 \times 2 = 12\). The expression is now simplified to: \(8 + 12\).

Step 4: Add

Finally, add 8 and 12 together: \(8 + 12 = 20\).

Key Concepts

Order of Operations

When evaluating arithmetic expressions, it’s crucial to follow the correct sequence of operations to arrive at the right answer. This sequence is known as the 'Order of Operations'. Always remember the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This guideline helps you know which operations to perform first.
For instance, in the expression given (8 + 6(5-3)), you first need to handle the parentheses. Once the expression inside the parentheses is simplified, you proceed to multiplication, and finally, any remaining addition or subtraction.

Parentheses

Parentheses are used in arithmetic expressions to indicate which operations should be performed first. They play a crucial role when adhering to the order of operations. In our example, evaluate the inside of the parentheses first: (5-3). This simplifies to 2.
Once you’ve simplified inside the parentheses, remove them and continue solving the expression. Now, our expression looks like this: 8 + 6(2). Notice we still need to perform multiplication before addition.

Multiplication

Multiplication comes after dealing with any parentheses and exponents in an expression. Once you’ve simplified inside any parentheses, you check for and perform any multiplications. For our expression: (8 + 6(2)), the next step is to multiply 6 by 2. So, 6 × 2 = 12.
This step helps to break down complex expressions into simpler ones, making it easier to then move on to any addition or subtraction.

Addition

Addition, along with subtraction, is the last operation you perform according to the order of operations. In our example, we are left with a simplified expression: 8 + 12. Now, simply add these two numbers together to get the final result: 20.
Following these steps systematically ensures that you get the correct result without making mistakes.