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Chapter 6: Problem 42

Use the distributive property to rewrite each expression without parentheses. $$ -(3 n-4) $$

Short Answer

Expert verified
-3n + 4

Step by step solution

01

- Identify the expression

The expression given is o (3n - 4). The goal is to rewrite this expression without the parentheses using the distributive property.
02

- Apply the Distributive Property

The distributive property states that a(b + c) = ab + ac. In this case, the -o will be distributed to each term inside the parenthesis (3n - 4). So, o(3n - 4) = o(3n)+ o( -4).
03

- Simplify Each Term

Simplify each term by multiplying o by 3n and 4. So: o(3n) = -3n, o(-4) = +4.
04

- Combine the Results

Combine the simplified terms into a single expression without parentheses: -3n + 4.

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Key Concepts

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

Simplifying Expressions
Simplifying expressions in algebra is like cleaning up a messy room.
You want to make everything as clear and organized as possible.
When you're given an expression with parentheses, like \(-(3n - 4)\), your first step is to eliminate the parentheses using algebraic rules.
This process is often easier if we use the Distributive Property, especially when we need to handle various operations.
Once we've distributed and combined like terms, our expression becomes neat and tidy.
For our example, applying this would turn \(-(3n - 4)\) into \(-3n + 4\).
Practicing these steps can make complicated problems much easier to solve.
Algebraic Operations
Algebraic operations are the basic building blocks for manipulating expressions.
These include addition, subtraction, multiplication, and division.
When dealing with expressions inside parentheses, multiplication is usually key.
For instance, in the expression \(-(3n - 4)\), we use the multiplication part of the Distributive Property: \(a(b + c) = ab + ac\).
Here, we multiply \(-1\) (hidden as the lone negative sign) by each term inside the parenthesis.
So, \(-1 \times 3n = -3n\) and \(-1 \times -4 = +4\).
It's important to multiply correctly and keep track of positive and negative signs.
After all operations, always combine like terms to finish simplifying the expression.
Negative Coefficients
Negative coefficients can sometimes be tricky but they follow simple rules.
A negative coefficient just means we're dealing with multiplication by a negative number.
In our example, \(-(3n - 4)\), the negative sign in front of the parenthesis acts as \(-1\).
This means every term inside the parentheses is multiplied by \(-1)\).
Remember, a negative times a positive gives a negative result: \(-1 \times 3n = -3n\).
Conversely, a negative times a negative gives a positive result: \(-1 \times -4 = +4\).
Always be mindful of these rules to avoid mistakes.
Clearly marking your steps can help avoid confusion when simplifying expressions with negative coefficients.

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