One-Step Equation

Definition

A one-step equation is a simple algebraic equation that can be solved in a single step, typically involving only one operation such as addition, subtraction, multiplication, or division. These equations are foundational in the study of solving equations using the properties of equality.

5 Must Know Facts For Your Next Test

1. One-step equations can be solved by isolating the variable through a single operation, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
2. Solving one-step equations is a fundamental skill that lays the groundwork for solving more complex multi-step equations.
3. The properties of equality, such as the addition and subtraction properties, are essential for solving one-step equations by maintaining the balance between the two sides of the equation.
4. One-step equations often involve simple operations with integers, fractions, or decimals, making them a crucial stepping stone in the development of algebraic problem-solving skills.
5. Mastering the techniques for solving one-step equations prepares students for the more advanced concepts of solving multi-step equations and systems of equations.

Review Questions

• Explain how the properties of equality are used to solve a one-step equation.
  • To solve a one-step equation, the properties of equality are used to isolate the variable on one side of the equation. This is done by performing the same operation (addition, subtraction, multiplication, or division) on both sides of the equation, maintaining the balance and ensuring that the variable is the only term remaining on one side. For example, to solve the equation $5x = 20$, the addition property of equality would be used to divide both sides by 5, resulting in the solution $x = 4$.
• Describe the relationship between one-step equations and the development of algebraic problem-solving skills.
  • One-step equations serve as a fundamental building block in the progression of algebraic problem-solving skills. Mastering the techniques for solving these simple equations lays the groundwork for students to tackle more complex multi-step equations and systems of equations. The ability to isolate variables and maintain the balance of an equation through the application of the properties of equality is a critical skill that students must develop. Proficiency in solving one-step equations prepares students to tackle higher-level algebraic concepts and apply their problem-solving abilities to a wide range of mathematical situations.
• Evaluate the importance of one-step equations in the context of the broader study of solving equations using the properties of equality.
  • One-step equations are a crucial component in the study of solving equations using the properties of equality. They provide a solid foundation for students to understand the underlying principles and techniques involved in equation-solving. By mastering the skills required to solve one-step equations, students develop a deeper comprehension of the properties of equality and how they can be applied to maintain the balance of an equation. This knowledge serves as a springboard for tackling more complex multi-step equations and systems of equations, which build upon the concepts learned through one-step equations. The ability to isolate variables and perform the necessary operations to find solutions is a fundamental algebraic skill that is essential for success in higher-level mathematics. Therefore, the study of one-step equations is a vital part of the broader curriculum on solving equations using the properties of equality.

Related terms

Equation:

An equation is a mathematical statement that shows two expressions are equal, often containing variables that need to be solved for.

Properties of Equality: The properties of equality are the rules that govern how the equal sign (=) can be manipulated in an equation, such as adding, subtracting, multiplying, or dividing both sides by the same value.

Variable:

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