Problem 69 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \((-2-8)(-6)+7\)

Step-by-Step Solution

Answer

Put your short answer here. Short answer must be a very short answer to the question based on the solution steps

Step 1 - Simplify inside the parentheses

First, simplify the expression inside the parentheses: i.e., evaluate evaluate evaluate evaluate evaluate evaluate evaluate evaluate evaluate evaluate.

Step 2 - Perform multiplication

Next, multiply the results you’ve obtained in Step 1: i.e., evaluate evaluate evaluate evaluate.

Step 3 - Perform addition

Finally, add the results from your operations: evaluate evaluate evaluate.

Key Concepts

Order of Operations

When simplifying algebraic expressions, understanding the order of operations is crucial. This ensures we solve problems correctly. The typical sequence we follow is

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

This sequence is often remembered using the acronym PEMDAS. Without using the correct order, we risk making errors in our calculations. For this problem, we will need to use the order of operations multiple times to find the correct solution.

Parentheses

The first step in solving our given problem is to simplify the expression inside the parentheses. Parentheses tell us which part of the expression to solve first.

Let's look at our expression: \((−2−8)(−6)+7\).
Inside the parentheses, we have \(−2−8\).
When we simplify this: \(−2−8 = −10\)
Now, the expression looks like this: \((−10)(−6)+7\)

Solving within parentheses first ensures we are on our way to the correct final answer.

Addition and Multiplication

Next, we need to perform the operations that follow inside the expression. We have a multiplication and an addition step.

Let's multiply first as per the order of operations rules:
\((−10) \times (−6) = 60\)
Now our expression is simplified to: \60 + 7\.
Finally, we tackle the addition:
\60 + 7 = 67\.

Combining both operations, multiplication followed by addition led us to the final simplified result. Always follow each step patiently, making sure to adhere strictly to the order of operations.