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Chapter 3: Problem 81

Clear parentheses and combine like terms. $$-3-(2 n+1)$$

Short Answer

Expert verified
-4 - 2n

Step by step solution

01

- Distribute the Negative Sign

Start by distributing the negative sign across the terms inside the parentheses. This means multiplying (-1) by each term inside the parentheses. So, - (2n + 1) becomes -2n - 1.
02

- Write the Expression Without Parentheses

Now, rewrite the original expression without the parentheses, using the distributed terms: -3 - 2n - 1.
03

- Combine Like Terms

Combine the constant terms together: -3 - 1 = -4.Now, rewrite the expression: -4 - 2n.

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Key Concepts

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

Distributive Property
The distributive property is an essential concept in algebra. It allows you to multiply a single term by each term inside a set of parentheses. In the given exercise, we distribute the negative sign across the terms inside the parentheses. This means we convert - (2n + 1) to -2n - 1. Think of it like spreading the negative sign to each term inside. Here's how you do it step-by-step:
  • Identify the terms inside the parentheses.
  • Multiply each term by -1 (since the negative sign outside the parentheses is equivalent to multiplying by -1).
  • Replace the original terms with the new terms.
When you distribute correctly, complex expressions become simpler and easier to manage.
Combining Like Terms
Combining like terms is a crucial part of simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. For instance, in the expression -3 - 2n - 1, we combine the constant terms -3 and -1.To combine like terms, follow these steps:
  • Identify the like terms in your expression.
  • Add or subtract the coefficients (the numbers) of these terms.
  • Rewrite the expression using the simplified terms.
In our example, we combine -3 and -1 to get -4. This simplifies the expression to -4 - 2n. Combining like terms helps in reducing the expression to its simplest form and makes it easier to understand and solve.
Negative Numbers in Algebra
Handling negative numbers correctly is vital in algebra. It can often be a tricky part for students. When dealing with negative numbers, especially in operations like addition and subtraction, remember to think in terms of gains and losses. Here are some tips to simplify working with negative numbers:
  • When adding a negative number, it's the same as subtracting its positive counterpart. For example, -3 + (-1) is the same as -3 - 1.
  • Subtracting a negative number is like adding its positive counterpart. For example, -4 - (-2) is the same as -4 + 2.
  • Always pay attention to the signs during multiplication and division: multiplying or dividing two negative numbers results in a positive number, while multiplying or dividing a positive and a negative number results in a negative number.
In our exercise, we use these principles when we distribute the negative sign and combine like terms. It ensures the expression is correctly simplified, leading to the final simplified form of -4 - 2n.

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