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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 \(6w \).

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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.

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