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Chapter 1: Problem 19

In each term, give the numerical coefficient of the variable(s). $$ -x $$

Short Answer

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Step by step solution

01

Identify the variable

In the given term -x , identify the variable. The variable here is x.
02

Identify the term associated with the variable

Observe that x is preceded by a negative sign. This means you have the term -x.
03

Extract the numerical coefficient

The numerical coefficient is the number multiplying the variable x. If there is no number written, it is understood to be 1. Since it is preceded by a negative sign, the numerical coefficient is -1.

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Key Concepts

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

Variables in Algebra
In algebra, variables stand for unknown values. They can be any letter, but commonly we use letters like x, y, or z. Variables can change, which is why we call them 'variables.' When you see a term like -x, the 'x' itself is the variable.
Understanding variables is crucial because they help you solve equations and understand mathematical relationships. Here are some key points:
  • A variable represents an unknown quantity.
  • It can be any letter or symbol.
  • Variables allow us to create general formulas and solve problems systematically.
If you see -x in a problem, the x is the part you're usually solving for or working with.
Negative Sign in Algebra
The negative sign (-) in algebra can change the value of a variable or number. It's important to pay close attention to these signs because they affect the overall calculation.
For instance, in the term -x, the negative sign means you are dealing with the opposite of x. Here are a few tips to help you understand negative signs:
  • A positive number is greater than zero.
  • A negative number is less than zero.
  • A negative sign in front of a term reverses its sign.
So, -1 is the opposite of +1, and -x is the opposite of +x. This is especially important when working with equations and expressions.
Understanding Algebraic Terms
In algebra, terms are the building blocks of expressions and equations. A term is a number, a variable, or a combination of both multiplied together. Let's break down the term -x:
  • Numerical Coefficient: This is the number part of the term that multiplies the variable. In -x, the numerical coefficient is -1 because it is understood that any variable without an explicit coefficient has a coefficient of 1.
  • Variable: This is the letter part, which in this case is x.
  • Negative Sign: Indicates that the term is negative.
By understanding the components of a term, you can better grasp how to manipulate and solve algebraic expressions. For instance, in the term -x, knowing that the numerical coefficient is -1 helps you understand how the term behaves in equations.

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