/*! 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 11 Add or subtract the monomials. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 11

Add or subtract the monomials. $$-12 w+18 w$$

Short Answer

Expert verified
The result is \(6w \).

Step by step solution

01

- Identify Like Terms

Determine if the terms involved are like terms. Like terms have the same variable raised to the same power. In this exercise, \( -12w \) and \( 18w \) are like terms because they both contain the variable \(w\) raised to the first power.
02

- Combine the Coefficients

Since the terms are like terms, combine them by adding or subtracting their coefficients. The coefficients are \(-12\) and \(18\). Perform the addition: \(-12 + 18 \).
03

- Compute the Result

Calculate \(-12 + 18 \), which is \(6 \). Therefore, the result of combining the terms \(-12w + 18w \) is \(6w \).

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
To combine monomials through addition or subtraction, you need to first identify like terms. Like terms are terms in an algebraic expression that have the same variable raised to the same power. For instance, in the problem -12w + 18w, both terms contain the variable w raised to the first power. Thus, they are like terms and can be combined. Remember, terms like w and w^2 are not like terms because the exponents differ. This is a crucial step to ensure you are correctly adding or subtracting terms in algebra.
coefficients
Once you've identified like terms, the next step is to work with their coefficients. The coefficient is the numerical part of the term that is multiplied by the variable. In our example, the coefficients are -12 and 18. To combine like terms, you simply add or subtract these coefficients as the equation dictates. Combining the coefficients -12 and 18 in the problem gives us: \(-12 + 18 = 6\). So, the resulting term will be 6w. This process allows you to simplify algebraic expressions and make them easier to work with.
algebraic expressions
An algebraic expression is a mathematical phrase that includes numbers, variables, and operators (like addition and subtraction). For example, the expression -12w + 18w consists of two terms linked by an addition operator. Simplifying algebraic expressions by combining like terms is a fundamental skill in algebra. This process makes more complicated expressions easier to manage and solve. Always remember to:
- Identify like terms
- Combine their coefficients
- Simplify the expression.
In the given problem, combining like terms resulted in the simplified algebraic expression: 6w. Understanding these steps is key to mastering algebra.

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

When Drake simplified \(-3^{0}\) and \((-3)^{0}\) he got the same answer. Explain how using the Order of Operations correctly gives different answers.

Divide the monomials. $$\frac{\left(4 u^{2} v^{5}\right)\left(15 u^{3} v\right)}{\left(12 u^{3} v\right)\left(u^{4} v\right)}$$

Divide each polynomial by the monomial. $$\left(9 n^{4}+6 n^{3}\right) \div 3 n$$

Divide each polynomial by the binomial. $$\left(y^{2}-3 y-15\right) \div(y-8)$$

Mixed Practice (a) \(p^{4} \cdot p^{6}\) (b) \(\left(p^{4}\right)^{6}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.