/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 26 Simplify the expression. $$-(-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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

01

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 \[6y - 9x + 7\].
02

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

Most popular questions from this chapter

Simplify the expression by first using the distributive property to expand the expression, and then rearranging and combining like terms mentally. $$3(8 r-7)-3(2 r-2)$$

Simplify the expression. $$-(-3 y-4+4 x)$$

Even numbers. Evaluate the expression 2n for the following values: i) n = 1 ii) n = 2 iii) n = 3 iv) n = ?4 v) n = ?5 vi) Is the result always an even number? Explain.

Solve the equation. $$-8 x-5(x-3)=15$$

Use the associative and commutative properties of multiplication to simplify the expression. $$(-8 x)(-5)$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.