/*! 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 9 For exercises 1-66, simplify. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 9

For exercises 1-66, simplify. $$ \frac{2 x-8}{10} $$

Short Answer

Expert verified
The simplified form is \(\frac{x - 4}{5}\).

Step by step solution

01

Identify common factors

Look at the numerator to see if there is a common factor that can be factored out. The numerator is \(2x - 8\), and both terms in the numerator have a common factor of 2.
02

Factor the common term

Factor 2 out of the terms in the numerator: \[2(x - 4)\]
03

Rewrite the fraction

Rewrite the original fraction \(\frac{2x - 8}{10}\) using the factored form: \[\frac{2(x - 4)}{10}\]
04

Simplify the fraction

Now simplify the fraction by canceling the common factor from the numerator and the denominator. The number 2 is common in both: \[\frac{2(x - 4)}{10} = \frac{2(x - 4)}{2 \times 5} = \frac{x - 4}{5}\]

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.

Factoring
Factoring is a technique used in algebra to simplify expressions. It involves breaking down a number or an expression into its composite parts, also known as factors. In the problem given, the numerator is \(2x - 8\). The first step is to identify common factors in this expression. Both 2x and 8 are divisible by the number 2. By factoring out the common term, we convert 2x - 8 into a simplified form: \[2(x - 4)\]. This process is crucial as it allows us to simplify more complex expressions with ease.
Numerator and Denominator
In a fraction, the numerator is the expression above the line, and the denominator is the expression below the line. For the fraction \( \frac{2x-8}{10} \), \(2x - 8 \) is the numerator, and 10 is the denominator. Understanding the roles of the numerator and denominator helps in simplifying fractions. In this example, we identified that both the numerator and the denominator can be factored. Once we factor the numerator, we rewrite the fraction as \[ \frac{2(x - 4)}{10} \].
Canceling Common Factors
Canceling common factors is a method used to simplify fractions. After factoring, we often find common factors in the numerator and the denominator that can be canceled out. In \[ \frac{2(x - 4)}{10} \], the common factor is the number 2. Division of both the numerator and the denominator by 2 simplifies the fraction: \[ \frac{2(x - 4)}{10} = \frac{2(x - 4)}{2 \times 5} = \frac{x - 4}{5} \]. This results in a simpler expression, \( \frac{x - 4}{5} \). This technique makes complex fractions much easier to manage.

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

For exercises \(35-36, T=\frac{336 \mathrm{gm}}{R}\) represents the relationship of tire diameter, \(T\); gear ratio, \(g\); speed, \(m\); and revolutions of the tire per minute, \(R\). Is the relationship of the given variables a direct variation or an inverse variation? $$ g \text { and } R \text { are constant; the relationship of } T \text { and } m \text {. } $$

For exercises 11-30, (a) solve. (b) check. $$ \frac{15}{4 z}+\frac{2}{3}=\frac{1}{24} $$

For exercises 79-82, (a) clear the fractions and solve. (b) check. $$ 1=\frac{7}{6} w+\frac{5}{12} $$

A student overdraws a bank account about five times each month. Predict the total overdraft fees the student will pay in 1 year. Chase's overdraft fees are \(\$ 25\) for the first fee each year, \(\$ 32\) for the next four and \(\$ 35\) after that. (Source: www.nytimes .com, Sept. 23, 2009)

For exercises \(35-36, T=\frac{336 \mathrm{gm}}{R}\) represents the relationship of tire diameter, \(T\); gear ratio, \(g\); speed, \(m\); and revolutions of the tire per minute, \(R\). Is the relationship of the given variables a direct variation or an inverse variation? $$ g \text { and } m \text { are constant; the relationship of } T \text { and } R $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.