/*! 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 52 Rewrite each expression using th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 52

Rewrite each expression using the distributive property. Simplify if possible. $$-7(2-6)$$

Short Answer

Expert verified
The given expression $$-7(2-6)$$ can be rewritten using the distributive property as \(-7(2) + (-7)(-6)\), which simplifies to \(-14 + 42 = 28\).

Step by step solution

01

Apply the Distributive Property

First, apply the distributive property to the given expression, $$-7(2-6)$$. According to the distributive property, we can rewrite this expression as: \(-7(2) + (-7)(-6)\)
02

Multiply

Now, perform the multiplication operations in the rewritten expression: \(-14 + 42\)
03

Simplify

Next, simplify by adding the two numbers: \(-14 + 42 = 28\) So, $$-7(2-6)$$ can be rewritten and simplified as \(28\).

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.

Simplifying Expressions
When simplifying expressions, the goal is to make them as simple as possible by performing basic arithmetic operations. In the context of algebra, it often involves combining like terms and performing any operations indicated. The key is to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

For our example,
  • we first used the distributive property to break down the expressions within parentheses, which allowed us to simplify step-by-step.
  • Then, the expressions were calculated individually and combined to complete the simplification.
In this way, complex algebraic expressions become manageable and easier to understand.
Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operations. They are the building blocks of algebra, representing problems and relationships in mathematical form. An algebraic expression can be as simple as a number or variable, or more complex, involving operations and multiple terms.

In the given problem,
  • the expression \(-7(2-6)\) represents an algebraic expression that uses both numbers and the operation of multiplication.
  • Understanding the structure of this expression, including identifying terms and operations, is crucial in correctly simplifying it.
Recognizing these elements helps apply rules like the distributive property effectively, leading to the correct simplification.
Basic Algebra Operations
Basic algebra operations are the fundamental skills necessary for working with algebraic expressions. They include addition, subtraction, multiplication, and division, as well as the application of more specific rules like the distributive property.

For our exercise,
  • we used multiplication when applying the distributive property, which involves distributing the \(-7\) across each term inside the parentheses.
  • This involved multiplying \(-7\) by both \(2\) and \(-6\), resulting in two separate products.

To complete the solution, addition was used to add these products together. These basic operations are essential for building a strong foundation in algebra and enabling more complex problem-solving.

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

Write an expression for each and simplify. Answer the question with a complete sentence. In \(2002,\) the total attendance at Major League Baseball games was \(67,859,176 .\) In \(2003,\) that figure was \(67,630,052 .\) What was the difference in the number of people who went to ballparks from 2002 to \(2003 ?\)

Write a mathematical expression for each and simplify. 18 less than the sum of \(-5\) and 11.

Write an expression for each and simplify. Answer the question with a complete sentence. The median income for a male 25 years or older with a bachelor's degree in 2004 was \(\$ 51,081 .\) In \(2005,\) the median income was \(\$ 51,700 .\) What was the difference in the median income from 2004 to \(2005 ?\)

Write a mathematical expression for each and simplify. Twice the sum of 18 and \(-31\)

Rewrite each expression using the distributive property. Simplify if possible. $$2(-6+5+3)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.