Equality

Definition

Equality is a fundamental concept that describes the state of being equal, where individuals or objects have the same value, status, rights, or opportunities. It is a central idea in mathematics, particularly in the context of linear equations, where the equality sign represents the balance or equivalence between the expressions on both sides of the equation.

5 Must Know Facts For Your Next Test

1. In the context of linear equations, the equality sign ( $= $) represents the balance or equivalence between the expressions on both sides of the equation.
2. Solving a linear equation involves finding the value of the variable that makes the equation true, ensuring that the expressions on both sides are equal.
3. The properties of equality, such as the reflexive, symmetric, and transitive properties, are essential in manipulating and solving linear equations.
4. Maintaining the equality of an equation is crucial when performing operations like addition, subtraction, multiplication, or division to isolate the variable and find its value.
5. Understanding the concept of equality is fundamental in understanding and applying the principles of solving linear equations in one variable.

Review Questions

• Explain how the equality sign ( $= $) is used in the context of linear equations in one variable.
  • In the context of linear equations in one variable, the equality sign ( $= $) represents the balance or equivalence between the expressions on both sides of the equation. The equality sign indicates that the left-hand side and the right-hand side of the equation have the same value, and it is the primary way to express the relationship between the variable and the constants in the equation. Maintaining this equality is crucial when solving the equation, as any operations performed on one side must be applied to the other side to preserve the balance and find the value of the variable.
• Describe the properties of equality and how they are used in solving linear equations in one variable.
  • The properties of equality, which include the reflexive, symmetric, and transitive properties, are essential in manipulating and solving linear equations in one variable. The reflexive property states that any expression is equal to itself, the symmetric property states that if $A = B $, then $B = A $, and the transitive property states that if $A = B $ and $B = C $, then $A = C $. These properties allow you to perform various operations on the equation, such as adding, subtracting, multiplying, or dividing both sides, while maintaining the equality and isolating the variable to find its value.
• Analyze the role of the concept of equality in the process of solving linear equations in one variable.
  • The concept of equality is fundamental to the process of solving linear equations in one variable. The equality sign ( $= $) represents the balance between the expressions on both sides of the equation, and maintaining this equality is crucial throughout the solution process. By performing operations that preserve the equality, such as adding, subtracting, multiplying, or dividing both sides of the equation, you can isolate the variable and find its value. Understanding the properties of equality, including the reflexive, symmetric, and transitive properties, allows you to manipulate the equation in a way that ensures the equality is maintained, leading to the successful solution of the linear equation.

Related terms

Equation:

An equation is a mathematical statement that asserts the equality of two expressions, typically involving variables and constants, connected by an equals sign.

Variable:

A variable is a symbol, usually a letter, that represents an unknown or changeable quantity in an equation or expression.

Constant:

A constant is a fixed value that does not change within a given context or problem.