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Chapter 2: Problem 54

Find the terms of the expression. \(9-28 x\)

Short Answer

Expert verified
The terms of the expression \(9-28x\) are '9' and '-28x'.

Step by step solution

01

Identify the operation

The first thing to do is to identify what type of operation is included in the expression. Here, the operation is subtraction, which is denoted by the '-' sign.
02

Separate the terms using the operation

The operation sign splits the expression into different terms. Mathematically speaking, a term can be a single number, a variable, or numbers and variables combined through multiplication or division. The subtraction operation here separates the expression \(9-28x\) into two terms.
03

Identify the terms

From the analysis above, we find that the two terms separated by the subtraction operation are '9' and '-28x'.

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Key Concepts

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

Understanding Terms in Algebraic Expressions
In algebra, a \"term\" refers to a single mathematical expression. It could be a number, a variable, or a product of numbers and variables. Terms can be combined by operations such as addition or subtraction to form an algebraic expression. Recognizing and separating these terms is crucial in solving and simplifying expressions.

For example, in the expression \(9-28x\), there are two distinct terms. The first is \(9\), a constant term, and the second is \(-28x\), which includes both a number and a variable. Each term in the expression can be handled separately for calculations, which makes understanding the concept of terms foundational to algebra.
Exploring Subtraction in Algebra
Subtraction is one of the fundamental operations in mathematics, symbolized by the minus sign \(-\). In an algebraic expression, subtraction acts as a separator of terms, allowing us to identify and handle each part independently.

In our expression \(9-28x\), subtraction helps us split the two components into separate entities: the constant \(9\) and the term involving a variable \(-28x\). It's important to note that when subtraction is involved, the sign of the subsequent term (here, \(-28x\)) is taken as negative. Understanding subtraction in this manner is key to mastering algebraic manipulations.
Unpacking Variables in Algebra
Variables are symbols used to represent unknown values in mathematics, often denoted by letters such as \(x\), \(y\), or \(z\). They are essential in forming algebraic expressions, equations, and functions.

In our expression \(9-28x\), the variable \(x\) allows the expression to represent a relationship rather than a single fixed value. This variable is part of the term \(-28x\), where \(-28\) is its coefficient, indicating how much "influence" the variable has in that term. Emphasizing the role of variables helps in deducing patterns, solving equations, and understanding mathematical relationships more deeply.

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Most popular questions from this chapter

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -y\left(-y^{2}+y\right) $$

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 107 a-208 a $$

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 3 x^{2}+2 x^{2}-7 $$

Evaluate the expression. $$ 89-8 \cdot 5-27 $$

EXPRESSIONS WITH FRACTION BARS Evaluate the expression. $$ \frac{6+7^{2}}{3^{3}-9-7} $$
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