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Chapter 4: Problem 4

Classify the following equations in terms of their degree. $$ x=9 $$

Short Answer

Expert verified
Answer: The degree of the equation $$x=9$$ is 1, making it a first-degree or linear equation.

Step by step solution

01

Identify the variables and their powers in the equation

In the given equation $$x=9$$, the variable is x and its power is 1 (since x is same as x to the power 1, or $$x^1$$).
02

Determine the highest power of the variable in the equation

Since there is only one term containing the variable x with a power of 1, the highest power of the variable in the equation is 1.
03

Classify the equation based on its degree

The degree of an equation is the highest power of the variable present in the equation. In this case, the highest power of the variable is 1, which means that the degree of the equation $$x=9$$ is 1. This makes it a first-degree equation, also known as a linear equation.

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Key Concepts

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

Degree of an Equation
The degree of an equation is a key concept in understanding linear equations. Simply put, the degree is the highest power of the variable present in the equation. For example, in the equation \(x = 9\), the variable \(x\) has a power of 1. Conversely, if you have an equation like \(x^2 = 4\), the degree would be 2 because the highest power of the variable is 2.
The degree gives us critical information about the type of equation we are dealing with. For instance:
  • A first-degree equation (degree 1) is a linear equation.
  • A second-degree equation (degree 2) is a quadratic equation.
  • A third-degree equation (degree 3) is a cubic equation, and so on.
Recognizing the degree of an equation helps us understand its properties and solutions, which can greatly assist in solving more complex problems.
Variable Identification
Variable identification is the process of determining which symbol in an equation represents a quantity that can change or vary. In mathematics, this is typically a letter like \(x\), \(y\), or \(z\). Identifying the variable in an equation is crucial because it is the part of the equation that you can solve for or manipulate.
In the equation \(x = 9\), \(x\) is the variable, which is often referred to as an unknown. When solving an equation, you are usually trying to find the value of this variable.
To effectively identify variables:
  • Look for the symbol(s) which you need to find or change their values.
  • These symbols are usually the ones we differentiate from numbers and constants, such as \(9\) in our example.
Understanding variable identification lays the foundation for correctly approaching and solving equations.
Power of a Variable
The power of a variable refers to the exponent attached to it, which indicates how many times the variable is multiplied by itself. This is fundamental in determining the behavior and type of an equation. For instance, consider the expression \(x^1\), the power is 1, indicating \(x\) is used once. Similarly, \(x^2\) signifies that \(x\) is multiplied by itself, so \(x \,\times\, x\).
The power impacts the equation by:
  • Determining its degree, as the highest power defines whether it's linear, quadratic, etc.
  • Affecting how you solve the equation since different powers require different solution methods.
  • Indicating the type of graph the equation will create when visualized. For instance, \(x^1\) creates a straight line, unlike \(x^2\) which forms a curve.
Grasping the power of a variable is essential for mastering the basics of algebra and for solving equations of any level.

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Most popular questions from this chapter

List, if any should appear, the common factors for the following problems. $$ 17 x^{2} y(z+4)+51 y(z+4) $$

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Find the product. \((4 x+3)(4 x-3)\).

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