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Chapter 2: Problem 12

Find the terms of the expression. $$ 12-5 x $$

Short Answer

Expert verified
The terms of the expression \(12 - 5x\) are '12' and '-5x'

Step by step solution

01

Identify the terms

In the expression, \(12 - 5x\), '+' or '-' separate the terms. Here, '-' is used, implying we have two terms. So the first term is '12' and the second term is '-5x'.

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Key Concepts

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

Terms in Algebra
In algebra, terms are the building blocks of mathematical expressions. A term can be a number, a variable, or a combination of both multiplied together. Terms are separated by plus "+" or minus "-" signs in an expression. For example, in the expression \(12 - 5x\), we have two terms. Understanding terms is essential because they help us simplify and solve complex expressions.Terms can be classified as:
  • Constant Terms: These are numbers without any variables. In our example, \(12\) is a constant term.
  • Variable Terms: These include variables possibly multiplied by numbers, which are called coefficients. In \(5x\), "5" is the coefficient and "x" is the variable.
Being able to distinguish between these types of terms helps in the simplification and manipulation of expressions.
Mathematical Expressions
Mathematical expressions represent a combination of numbers, variables, and operations, like addition or subtraction. They do not have an equality sign, unlike equations. Expression is a broad term and can range from simple expressions containing a single term to complex ones with multiple terms.In the expression \(12 - 5x\), we see combined terms creating a meaningful mathematical phrase. Here are some crucial points about mathematical expressions:
  • No Equal Sign: Unlike equations, expressions do not suggest any equality or balance.
  • Operations Involved: Operations may include addition, subtraction, multiplication, and division.
  • Simplification: Expressions can often be simplified to make them more manageable or to prepare them for solving in equations.
Understanding mathematical expressions is foundational to exploring algebra further and solving more complex algebraic problems.
Identifying Terms
Identifying terms in a mathematical expression is a crucial skill when working with algebra. To locate the terms, observe the operators (like '+' or '-') that separate them. Let's analyze how this works using our example expression \(12 - 5x\).
  • Operators as Separators: In \(12 - 5x\), the '-' sign acts as a separator. It divides the expression into two distinct parts.
  • Listing Terms: Preceding or following these operators will be the different terms in the expression. Hence, the terms are \(12\) and \(-5x\).
  • Sign Awareness: Be conscious of the sign (positive or negative) associated with each term. Here, while \(12\) is positive, \(5x\) takes a negative sign due to the '-' operator.
By mastering the skill of identifying terms, you set a strong foundation for simplifying and solving algebraic expressions.

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Most popular questions from this chapter

Evaluate the expression. $$ (27 \div 9) \div(7-5) $$

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ Simplify the left side of the inequality.

LEAVING A TIP In Exercises \(83-85\), use the following information. You and a friend decide to leave a \(15 \%\) tip for restaurant service. You compute the tip, \(T,\) as \(T=0.15 C,\) where \(C\) represents the cost of the meal. Your friend claims that an easier way to mentally compute the tip is to calculate \(10 \%\) of the cost of the meal plus one half of \(10 \%\) of the cost of the meal. Simplify the equation. What property did you use to simplify the equation?

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -(y-9) $$

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