/*! 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 40 Simplify expression. \(-2 y+x+... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 40

Simplify expression. \(-2 y+x+3 y\)

Short Answer

Expert verified
The simplified expression is \(y + x\).

Step by step solution

01

Identify Like Terms

In the given expression \[-2y + x + 3y\]you need to identify like terms. Like terms are terms that have the same variable raised to the same power. Here, \(-2y\) and \(3y\) are like terms because they both have the variable \(y\). The term \(x\) is different and stands alone.
02

Combine Like Terms

Now, add the coefficients of the like terms together. For the like terms \(-2y\) and \(3y\), you add the coefficients \(-2\) and \(3\):\(-2 + 3 = 1\).So, \(-2y + 3y = 1y\) or simply \(y\).

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.

Like Terms
In algebra, like terms are expressions that have the same variables and are raised to the same power. Recognizing like terms is crucial when simplifying expressions because they can be combined to simplify calculations.
  • Same Variables: Terms must include the same variable. For instance, both \( -2y \) and \( 3y \) contain the variable \( y \).
  • Raised to the Same Power: The variables must have the same exponent. If \( y \) appears without an exponent, it's understood to be \( y^1 \).
When combining like terms, only the coefficients, the numerical part of the terms, are added or subtracted, not the variables. This helps to consolidate expressions into a simpler form that's easier to work with. In the example \( -2y + 3y\), since both terms include \( y \), you combine them by adding their coefficients, resulting in a simpler expression: \( y \).
Coefficients
Coefficients are numeric factors that multiply the variables in an algebraic expression. Understanding coefficients is crucial for simplifying expressions and solving equations.
  • Role of Coefficients: They dictate how many times a term's variable is taken into account. In \( -2y \), \( -2 \) is the coefficient: it shows that the term involves \( y \) two times negatively.
  • Combining Coefficients: When simplifying expressions, you add or subtract coefficients of like terms. For example, in the expression \( -2y + 3y \), add the coefficients \( -2 \) and \( 3 \) to get \( 1 \). Thus, \( -2y + 3y \) simplifies to \( 1y \) or simply \( y \).
Coefficients provide the magnitude and direction of the variable: positive coefficients add, while negative coefficients subtract. Grasping how coefficients function is foundational to mastering algebra.
Variables
Variables in algebra are symbols used to represent unknown or general values. They are the building blocks of algebraic expressions and equations.
  • Purpose of Variables: They allow us to formulate general rules in mathematics and express relationships between quantities.
  • Common Variables: Letters like \( x \), \( y \), and \( z \) are frequently used as variables.
Variables can take on different values, making expressions adaptable to various situations. When simplifying, the goal is to reduce the complexity of an expression while retaining the variable's symbolic nature. In the expression \( -2y + x + 3y \), both \( y \) and \( x \) are variables. Recognizing the variable helps identify which terms can be combined and which stand alone, like \( x \) in this case. Understanding variables is key to solving equations and modeling real-life scenarios.

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 the Distributive Property to write each expression as an equivalent algebraic expression. $$4(j-k)$$

Find the next term in the pattern. $$326,344,362,380, \dots$$

An electrician charges \(\$ 35\) for a house call and \(\$ 80\) per hour for each hour worked. If the total charge was \(\$ 915\) to wire a new house, which equation would you use to find the number of hours \(n\) that the electrician worked? A \(35 n+2 n(80)=915\) B \(80+35 n=915\) C \(35+(80-n)=915\) D\( 35+80 n=915\)

You spend \(x\) minutes reading a book on Saturday. On Sunday, you spend 35 more minutes reading than you did on Saturday. Which expression represents the total amount of time spent reading the book on Saturday and Sunday? F. \(2 x+35\) H. \(2 x-35\) G. \(x+35\) J. \(x-35\)

Find sum. \(-5+4\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Applied 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.