Variable

Definition

A variable is a symbol, usually a letter, that represents an unknown or changeable quantity in an algebraic expression or equation. It is a fundamental concept in algebra that allows for the representation and manipulation of unknown or varying values.

5 Must Know Facts For Your Next Test

1. Variables are used to represent unknown or changing values in algebraic expressions and equations.
2. The value of a variable can be determined by solving an equation or system of equations that includes the variable.
3. Variables can be manipulated using the properties of equality, such as addition, subtraction, multiplication, and division.
4. The use of variables allows for the generalization of mathematical concepts and the representation of real-world problems.
5. Variables are essential in solving linear equations, inequalities, systems of equations, and various other algebraic problems.

Review Questions

• Explain how variables are used in the context of solving linear equations using the addition and subtraction properties of equality.
  • Variables are used in linear equations to represent unknown quantities. When solving linear equations using the addition and subtraction properties of equality, the goal is to isolate the variable on one side of the equation by performing the same operations on both sides. This allows the variable to be solved for, revealing its value. The use of variables in this context enables the generalization of the equation-solving process and the representation of a wide range of real-world problems involving unknown quantities.
• Describe the role of variables in solving systems of equations using the substitution method.
  • In a system of equations, variables represent the unknown quantities that need to be determined. The substitution method involves isolating a variable in one equation and then substituting its expression into the other equation(s) to solve for the remaining variable(s). This process relies on the manipulation of variables to find the unique solution(s) that satisfy all the equations in the system. The ability to work with variables is crucial for understanding and applying the substitution method to solve systems of equations.
• Analyze how variables are used in the context of solving rational equations and evaluating direct and inverse variation relationships.
  • Variables are essential in the study of rational equations and variation relationships. In rational equations, variables are used to represent the unknown quantities in the numerator and denominator of the rational expression. Solving these equations requires manipulating the variables to isolate the unknown. Similarly, in direct and inverse variation problems, variables are used to represent the quantities that are proportionally related. Understanding how to work with variables is key to recognizing, setting up, and solving these types of algebraic problems involving proportional relationships.

Related terms

Constant: A constant is a fixed value that does not change within the context of a particular problem or expression.

Expression: An expression is a combination of variables, constants, and operations that represents a value or a relationship.

Equation: An equation is a statement that two expressions are equal, often containing one or more variables that need to be solved for.