/*! 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 96 Translate to an algebraic expres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 96

Translate to an algebraic expression. $$ \\{x | x=2 n, n \text { is an integer }\\} $$

Short Answer

Expert verified
The algebraic expression is \(2n\).

Step by step solution

01

Identify the Set Description

The given set \(\{x | x = 2n, n \text{ is an integer }\}\) describes all numbers \(x\) that can be written as \(2n\), where \(n\) is any integer.
02

Understand the Role of \(n\)

Here, \(n\) is a variable representing any integer. This means \(n\) can take any integer value (e.g., -2, -1, 0, 1, 2, etc.).
03

Formulate the Algebraic Expression

Since \(x\) is defined as \(2n\), and \(n\) can be any integer, the algebraic expression for the set is simply \(2n\). This indicates a general even number.

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.

Set Notation
Set notation is a mathematical language used to describe and represent sets, which are collections of objects. In this exercise, the set is given by \( \{x | x=2 n, n \text { is an integer }\} \). This notation tells us that we are looking at a set of elements, specifically all numbers that can be expressed in the form of \(2n\), where \(n\) is an integer.

Here's the breakdown:
  • The curly braces \{ ... \} denote a set.
  • The symbol \textbar \ (read as 'such that') separates the elements from the condition they must satisfy.
  • The expression \( x = 2n \) describes the form of the elements in the set.
  • The phrase 'n is an integer' indicates the range of values that \( n \) can take.
Using set notation provides a clear, concise way to represent collections of numbers or objects that follow a specific rule.
Integers
Integers are a fundamental concept in math, representing whole numbers that can be positive, negative, or zero. They are denoted by \( \mathbb{Z} \). In this exercise, the variable \( n \) represents any integer, which means it can take on values like:

  • -3, -2, -1
  • 0
  • 1, 2, 3
Understanding that \( n \) can be any integer helps us realize that \( x \) can be any even number, as the expression \( x = 2n \) covers all possible values obtained by multiplying 2 with an integer.
Even Numbers
Even numbers are integers that are divisible by 2. In mathematical terms, an even number can be expressed as \( 2n \), where \( n \) is any integer.

Some key points about even numbers are:
  • They include both positive and negative integers, as well as zero (e.g., -4, -2, 0, 2, 4).
  • Every even number has a form where it can be expressed by multiplying 2 with another integer.
In the exercise, the set \( \{ x | x = 2n , n \text { is an integer }\} \) represents all these even numbers. Here, \( x = 2n \) tells us that any number \( x \) in this set must be an even number because it is obtained by multiplying an integer \( n \) by 2. This set is essentially the set of all even integers.

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 equivalent expression using the distributive law. $$ 7(x+1) $$

To the student and the instructor: Synthesis exercises are designed to challenge students to extend the concepts or skills studied in each section. Many synthesis exercises require the assimilation of skills and concepts from several sections. On a quiz, Mia answers \(6 \in \mathbb{Z}\) while Giovanni writes \(\\{6\\} \in \mathbb{Z} .\) Giovanni's answer does not receive full credit while Mia's does. Why?

Translate to an algebraic expression. \(\\{x | x=3 n, n \text { is a natural number }\\}\)

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ |-2-3| \cdot 4^{2}-3 $$

Calculate using the rules for order of operations. Find the greatest value of \(a\) for which \(|a| \geq 6.2\) and \(a<0\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and 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.