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Chapter 2: Problem 77

Simplify each expression. \(-(3 m+5)\)

Short Answer

Expert verified
-3m -5

Step by step solution

01

Understand the Expression

The given expression is \(-(3 m+5)\). It consists of a negative sign outside a parenthesis that contains the terms \(3m\) and \(5\).
02

Distribute the Negative Sign

Distribute the negative sign to both terms inside the parenthesis. This means multiplying \(-(3 m)\) and \(-(5)\).
03

Simplify Each Term

Simplify the multiplication for each term: \(-(3 m) = -3 m\) and \(-(5) = -5\).
04

Combine the Terms

Combine the simplified terms to get the final expression: \(-3 m-5\).

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Key Concepts

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

Simplification
Simplification is the process of reducing an expression to its most basic form. It involves performing the necessary algebraic operations to make the expression simpler and more compact. For example, given the expression \(-(3 m+5)\), our aim is to simplify it to its simplest form.

To do this, we follow a series of steps like distributing, combining like terms, and simplifying further if possible. Simplification helps us better understand and work with mathematical expressions.
Distributive Property
The distributive property is a fundamental concept in algebra that allows us to multiply a single term across terms inside parentheses. It states that \(a(b + c) = ab + ac\). This property is especially useful when simplifying expressions that involve parentheses.

In the given exercise, \(-(3 m+5)\), we use the distributive property to distribute the negative sign across both terms within the parentheses. This results in \(-3m - 5\).

The distributive property helps break down complex expressions into manageable pieces, making simplification easier.
Negative Sign Distribution
Negative sign distribution involves multiplying each term inside parentheses by a negative sign. This can be thought of as distributing the \(-1\) across each term. The negative sign changes the sign of each term in the expression.

For the expression \(-(3 m+5)\), we distribute the negative sign to both terms inside the parentheses: \(-(3 m)\) and \(-(5)\).

This gives us \(-3m\) and \(-5\) respectively. Combining these terms, we get the simplified expression \(-3m - 5\).

Understanding negative sign distribution is crucial when simplifying expressions involving negative parentheses.

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