One-Step Equations

Definition

A one-step equation is a linear equation that can be solved in a single step, typically involving only one operation such as addition, subtraction, multiplication, or division. These equations are the simplest form of linear equations and are often used to introduce students to the concept of solving equations.

5 Must Know Facts For Your Next Test

1. One-step equations can be solved by applying the division or multiplication property of equality to isolate the variable.
2. The division property of equality states that if $ax = b$, then $x = b/a$.
3. The multiplication property of equality states that if $x/a = b$, then $x = ab$.
4. One-step equations often involve solving for a variable in a simple linear expression, such as $3x = 12$ or $x/4 = 5$.
5. Solving one-step equations is a fundamental skill that prepares students for more complex linear equations and algebraic problem-solving.

Review Questions

• Explain how the division and multiplication properties of equality are used to solve one-step equations.
  • To solve a one-step equation using the division property of equality, you would divide both sides of the equation by the coefficient of the variable. For example, to solve $3x = 12$, you would divide both sides by 3 to get $x = 4$. Similarly, to solve an equation in the form $x/a = b$ using the multiplication property of equality, you would multiply both sides by $a$ to isolate the variable $x$. For instance, to solve $x/4 = 5$, you would multiply both sides by 4 to get $x = 20$. These inverse operations are used to isolate the variable and find its value.
• Describe the key differences between solving one-step equations and more complex linear equations.
  • The primary difference between solving one-step equations and more complex linear equations is the number of operations required. One-step equations can be solved in a single step by applying either the division or multiplication property of equality, whereas complex linear equations may require multiple steps, including combining like terms, using the distributive property, and applying inverse operations multiple times. Additionally, one-step equations typically involve simpler expressions with a single variable, while complex linear equations may have multiple variables and more complicated coefficient structures. The skills developed in solving one-step equations, however, provide a foundation for tackling more advanced linear equation solving.
• Explain how the ability to solve one-step equations contributes to a student's overall understanding of algebraic concepts and problem-solving.
  • Mastering the skill of solving one-step equations is a crucial step in developing a strong foundation in algebra. It teaches students the basic principles of equation solving, including the use of inverse operations and the properties of equality. These concepts are then built upon as students progress to solving more complex linear equations, systems of equations, and eventually, higher-order algebraic expressions. The ability to isolate a variable and find its value in a simple one-step equation lays the groundwork for students to apply these same strategies to tackle more challenging algebraic problems, ultimately enhancing their overall problem-solving skills and understanding of the underlying algebraic concepts.

Related terms

Linear Equation:

A linear equation is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants and $x$ is the variable.

Inverse Operations:

Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division. These operations are used to isolate the variable in an equation.

Equation Solving: Equation solving is the process of finding the value of the variable that makes the equation true. This involves using the properties of equality to perform the same operations on both sides of the equation.