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Chapter 6: Problem 20

Add or subtract the monomials. $$14 x-3 y-13 x$$

Short Answer

Expert verified
The simplified expression is \(x - 3y\).

Step by step solution

01

- Identify Like Terms

Examine the given expression: \(14x - 3y - 13x\). Look for terms that have the same variable and exponent.
02

- Group Like Terms

Group the terms with the same variable together. In this case, \(14x\) and \(-13x\) are like terms, while \(-3y\) is a different term.
03

- Perform the Operation on Like Terms

Combine the like terms by performing the subtraction: \(14x - 13x = 1x\) or simply \(x\).
04

- Write the Final Expression

Combine the result from the previous step with the remaining term: \(x - 3y\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

like terms
Like terms in algebra are terms that share the same variable and exponent. For example, in the expression \(14x - 3y - 13x\), the terms \(14x\) and \(-13x\) are like terms because they both contain the variable \(x\). In contrast, \(-3y\) is not a like term with the others since it contains a different variable, \(y\). Recognizing like terms is crucial because it allows you to combine them, simplifying the algebraic expression. When identifying like terms, pay close attention to both the variable and its exponent鈥攖hey must match for the terms to be combined.
combining like terms
Combining like terms simplifies algebraic expressions by consolidating terms with the same variables. In the given exercise \(14x - 3y - 13x\), the like terms \(14x\) and \(-13x\) can be combined. To do this, add or subtract their coefficients. Here, the operation is subtraction: \(14x - 13x = 1x\), which simplifies to \(x\). Importantly, \(-3y\) remains unchanged because it isn't like the \(x\) terms. Combining like terms makes the expression more manageable and sets up for further operations or final results.
algebraic expressions
Algebraic expressions are mathematical phrases that can contain numbers, variables, and operation symbols. They do not have an equals sign like algebraic equations. An example is \(14x - 3y - 13x\). Algebraic expressions are used to represent real-world problems where quantities vary. In algebra, simplifying these expressions鈥攍ike combining like terms鈥攊s common practice to make them easier to handle. This simplification helps in solving equations and understanding relationships between variables.
monomials
A monomial is an algebraic expression with just one term. In the context of the exercise, each part like \(14x\), \(-3y\), and \(-13x\) are individual monomials. They consist of a coefficient (a number) and variables raised to a power. For instance, in \(14x\), \(14\) is the coefficient, and \(x\) is the variable. To add or subtract monomials, their variables and exponents must match, making them like terms. Combining these monomials can simplify complex expressions, which is a fundamental skill in algebra.

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