Problem 26 Simplify the expression. $$-(-... [FREE SOLUTION]

91影视

Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 3: Problem 26

Simplify the expression. $$-(-6 y+9 x-7)$$

Short Answer

Expert verified

The expression simplifies to $6y - 9x + 7$.

Step by step solution

Distribute the Negative Sign

To simplify the expression $ -(-6y + 9x - 7) $, we need to distribute the negative sign across the terms inside the parentheses. This changes the sign of each term inside. Therefore: \[-6y + 9x - 7\] becomes \[6y - 9x + 7\].

Write the Simplified Expression

After distributing the negative sign, the simplified expression is obtained. You simply rewrite it without the parentheses: \[6y - 9x + 7\].

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Distributive Property

The distributive property is a foundation of algebra that helps make complex expressions more manageable. It involves multiplying a single term by each term in a parenthetical expression. In this case, the single term is the negative sign. When you encounter an expression like $-(-6y + 9x - 7)$, the negative sign has to be distributed across each term in the parentheses.
This means you change the sign of each term:

The $-6y$ becomes $6y$.
The $9x$ becomes $-9x$.
The $-7$ becomes $7$.

Learning how to distribute correctly ensures that you simplify expressions accurately and maintains balance in equations. Mastering this property is essential to advancing in algebra and beyond.

Simplifying Expressions

Simplifying expressions is a crucial skill in algebra that makes equations easier to work with. It involves reducing expressions to their simplest form while maintaining their original value. After utilizing the distributive property in our exercise, the expression $-(-6y + 9x - 7)$ becomes $[6y - 9x + 7]$.
Once you distribute and change the signs accordingly, the simplified expression should be properly organized:

Ensure all like terms are combined.
The expression should be free of unnecessary parentheses.

These steps result in a cleaner equation, which can simplify solving further mathematical problems.

Negative Numbers

Working with negative numbers is vital in algebra, as they often appear in various expressions and equations. They have unique properties that are essential to understand for correct mathematical operations.
When distributing a negative sign, such as in $-(-6y + 9x - 7)$, understanding negative numbers is crucial.

Negative times negative results in positive, which explains why $-(-6y)$ becomes $6y$.
Negative times positive results in negative, seen when $-9x$ is derived from $9x$.

Grasping how negative numbers influence other values in equations can reduce errors and increase your confidence in handling complex algebraic expressions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify the expression. $$-(-6 y+9 x-7)$$

Short Answer

Step by step solution

Distribute the Negative Sign

Write the Simplified Expression

Key Concepts

Distributive Property

Simplifying Expressions

Negative Numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Statistics

Pure Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.