/*! 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 151 Find an equivalent expression by... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 151

Find an equivalent expression by factoring. $$ 5 x+50 $$

Short Answer

Expert verified
5(x + 10)

Step by step solution

01

Identify the greatest common factor (GCF)

Look at the coefficients and constants in the expression. The terms are 5 and 50. The greatest common factor of 5 and 50 is 5.
02

Factor out the greatest common factor

Factor the identified GCF (5) out of each term in the expression. This means we need to express the original terms as a product of the GCF and another factor.\[ 5x + 50 = 5(x) + 5(10) \]
03

Write the factored expression

After factoring out the GCF (5), write the expression as the product of the GCF and the remaining terms in parentheses.\[ 5(x + 10) \]

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.

Greatest Common Factor (GCF)
The Greatest Common Factor, often abbreviated as GCF, is a key concept in the factoring process. The GCF of a set of terms is the largest number that divides all of them without leaving a remainder. For the expression given in the exercise, which is 5x + 50, you have to identify what number each term shares. In this case, both 5 and 50 are divisible by 5. So, the GCF is 5. Identifying the GCF is crucial because it allows you to simplify the original expression by pulling out this common factor.
Factoring Out the GCF
Once you have identified the GCF, the next step is to factor it out of each term in the expression. This means that you will express each term as a product of the GCF and another factor. Let's look at the terms in our exercise: 5x and 50. Given that the GCF is 5, you can rewrite each term:
  • 5x becomes 5(x)
  • 50 becomes 5(10)
Now, you have the expression written as a product of 5 and the remaining terms: 5(x) + 5(10). The final factored form is then achieved by taking out the common factor: 5(x + 10).
Equivalent Expressions
An equivalent expression is a different way of writing the same mathematical expression. The goal of factoring is to transform the original expression into a simpler or more useful form without changing its value. The expression 5(x + 10) is equivalent to 5x + 50 because, if you distributed the 5 back into the parentheses, you would return to the original expression. The benefit of working with equivalent expressions is that sometimes simpler forms make it easier to solve equations, graph functions, or understand the properties of the terms involved.

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

Use set-builder notation to write each set. The set of all even numbers between 9 and 99

The height and sides of a triangle are four consecutive integers. The height is the first integer, and the base is the third integer. The perimeter of the triangle is 42 in. Find the area of the triangle.

The number of animals adopted through Tallahassee Animal Services decreased \(1.1 \%\) from 2011 to \(2012 .\) It then decreased \(3.6 \%\) from 2012 to 2013 and decreased again \(8.5 \%\) from 2013 to \(2014 .\) The number increased \(11.0 \%\) from 2014 to \(2015 .\) If there were 2879 adoptions in \(2015,\) how many were there in \(2011 ?\)

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ \frac{4^{3}-(7-4)^{2}}{3^{2}-7} $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 43-(-9+2)^{2}+18 \div 6 \cdot(-2) $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.