/*! 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 30 In the following exercises, add ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 30

In the following exercises, add or subtract the monomials. Add: \(4 \mathrm{x}, 3 y,-3 x\)

Short Answer

Expert verified
\(x + 3y\)

Step by step solution

01

Identify Like Terms

First, identify the like terms. Like terms are terms that have the same variable part. In this case, the like terms are the terms with the variable 'x'.
02

Combine Like Terms

Add the coefficients of the like terms. Here, we have the terms: \(4x\) and \(-3x\). Add their coefficients: \(4 + (-3) = 1\).
03

Write the Result

Combine the results to write the final expression. The result is: \(1x + 3y\) or simply \(x + 3y\).

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.

Monomials
A monomial is a simple algebraic expression that consists of only one term. Each monomial is made up of a coefficient and a variable part.
For example, in the term \(4x\), the number 4 is the coefficient and \(x\) is the variable.
Monomials can only have non-negative integer exponents. This means you won鈥檛 see variables in the denominator or under a radical in a monomial.
Addition and Subtraction of Algebraic Expressions
When combining algebraic expressions, you need to focus on combining like terms.
Like terms are terms that have the same variable and the same exponent. For instance, \(3x\) and \(-5x\) are like terms because they both have the variable \(x\) to the first power.
To add or subtract, sum or subtract the coefficients of these like terms while keeping the variable part unchanged. If you have an expression like \(4x + 3y - 3x\), you first identify the like terms \(4x\) and \(-3x\).
After identifying the like terms, combine their coefficients: \(4 + (-3) = 1\), resulting in \(x\).
Thus, the expression becomes \(x + 3y\).
Coefficients
A coefficient is a number that multiplies a variable in an algebraic expression. It determines the magnitude or scaling factor for the variable part of the term. In the term \(7a\), 7 is the coefficient, showing how many times \(a\) is being multiplied.
When adding or subtracting terms, you're mainly working with coefficients to combine like terms.
For example, in the expression \(5x - 2x\), you subtract the coefficients (5 and 2) to get a result of \(3x\). Always handle the coefficients while keeping the variables and their exponents consistent.

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

Multiply the binomials. Use any method. $$ (3 r-8)(11 r+1) $$

Multiply each pair of conjugates using the Product of Conjugates Pattern. $$ (9 c-2 d)(9 c+2 d) $$

Find each product. $$ (p-3)(p+3) $$

Square each binomial using the Binomial Squares Pattern. $$ \left(3 x^{2}+2\right)^{2} $$

For functions \(f(x)=x^{2}-5 x+2\) and \(g(x)=x^{2}-3 x-1,\) find (a) \((f \cdot g)(x)\) (b) \((f \cdot g)(-1)\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Discrete 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.