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Chapter 1: Problem 84

Perform each indicated operation. $$ 6+(-9-2) $$

Short Answer

Expert verified
-5

Step by step solution

01

Understand the Expression

The given expression to solve is: $$ 6 + (-9 - 2) $$
02

Simplify Inside Parentheses

First, simplify the expression inside the parentheses ( ) Expression inside parentheses: $$ -9 - 2 $$ Combine these two numbers: $$ -9 - 2 = -11 $$
03

Simplify the Entire Expression

Now substitute $$ -11 $$ back into the expression: $$ 6 + (-11) $$ Then, add the two numbers: $$ 6 + (-11) = -5 $$
04

Write the Final Answer

The final simplified result is: $$ -5 $$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Parentheses in Algebra
In algebra, parentheses are used to group parts of an expression that need to be simplified first. This is essential because it tells you which operations to perform first.
Let's look at an example: **6 + (-9 - 2)**. Here, the numbers inside the parentheses, -9 and -2, have to be simplified before applying other operations.
By following the rule known as the 'order of operations', you handle what's inside the parentheses first. So, always start by simplifying the expression inside the parentheses before anything else.
Combining Integers
Understanding how to combine integers is crucial in algebra. Integers are whole numbers that can be either positive or negative. Combining them means either adding or subtracting these numbers.
In our example **6 + (-9 - 2)**, you first combine -9 and -2 inside the parentheses:
-9 - 2 = -11. This is because you are moving further in the negative direction on the number line.
Combining integers can be thought of as finding the difference. Just be careful with the signs. Practicing this is key to getting accurate results.
Simplifying Expressions
Simplifying an algebraic expression involves combining like terms and performing simple arithmetic operations.
In our example, after simplifying what's inside the parentheses, the expression becomes **6 + (-11)**.
Now, you only have to combine these two terms. Since one is positive (6) and the other is negative (-11), you essentially perform subtraction. The result is:
6 - 11 = -5.
Thus, the simplified expression is -5.
The key steps are to simplify within parentheses first, then combine any remaining terms, taking careful note of their signs. This will help you simplify any expression accurately.

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