Problem 23 In the following exercises, add ... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 23

In the following exercises, add or subtract the monomials. $$18 x-2 x$$

Short Answer

Expert verified

16x

Step by step solution

Identify like terms

First, notice that both terms, $18x$ and $-2x$, are like terms because they both have the same variable part, which is $x$.

Combine the coefficients

Add or subtract the coefficients of the like terms. Here, the coefficients are 18 and -2. Combine them by performing the operation: $18 - 2$.

Simplify the result

Perform the operation from Step 2: $18 - 2 = 16$. Thus, the simplified coefficient is 16. The expression combining these like terms is $16x$.

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

In algebra, understanding monomials is crucial to combining like terms. A monomial is an algebraic expression that consists of only one term. Examples of monomials include expressions like $5x$, $-3y$, or $7z^2$. Each monomial has two main parts: a coefficient and a variable part.

Recognizing monomials helps in identifying like terms. Like terms are monomials that have the same variable part. For instance, $18x$ and $-2x$ are like terms because their variable part is the same, which is $x$. Understanding this concept is the first step to combining like terms in an expression.

Coefficients

The coefficient is the numerical part of a monomial. It is the number that multiplies the variable. For example, in the monomial $18x$, 18 is the coefficient.

When combining like terms, we focus on the coefficients. We either add or subtract the coefficients, depending on the problem. In the exercise $18x - 2x$, the coefficients are 18 and -2. To combine like terms, we simply perform the operation indicated between these coefficients. Here, it means performing the subtraction $18 - 2$, which equals 16.

Simplification

Simplification is the process of making an expression easier to work with or understand. After combining the coefficients of like terms, the next step is to simplify the resulting expression.

Taking our previous example, we combined the coefficients 18 and -2 to get 16. Now, the expression $18x - 2x$ simplifies to $16x$.

Simplifying expressions helps in solving algebraic equations more efficiently. It involves reducing expressions to their simplest form without changing their value.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, add or subtract the monomials. $$18 x-2 x$$

Short Answer

Step by step solution

Identify like terms

Combine the coefficients

Simplify the result

Key Concepts

Monomials

Coefficients

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Probability and Statistics

Mechanics Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.