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 the starting point for students learning to solve equations.

5 Must Know Facts For Your Next Test

1. One-step equations can be solved using the addition, subtraction, multiplication, or division properties of equality.
2. The goal in solving a one-step equation is to isolate the variable by performing the inverse operation to both sides of the equation.
3. When solving one-step equations, it is important to perform the same operation to both sides of the equation to maintain the equality.
4. One-step equations are the simplest form of linear equations and are often the first type of equations students learn to solve.
5. Solving one-step equations helps build a foundation for solving more complex linear equations in the future.

Review Questions

• Explain how the addition and subtraction properties of equality can be used to solve one-step equations.
  • The addition and subtraction properties of equality state that the same number can be added to or subtracted from both sides of an equation without changing the equality. When solving a one-step equation that involves addition or subtraction, the goal is to isolate the variable by performing the inverse operation (subtraction or addition) to both sides of the equation. For example, to solve the equation $x + 5 = 12$, you would subtract 5 from both sides to get $x = 7$, isolating the variable $x$.
• Describe the process of using the multiplication and division properties of equality to solve one-step equations.
  • The multiplication and division properties of equality state that both sides of an equation can be multiplied or divided by the same non-zero number without changing the equality. When solving a one-step equation that involves multiplication or division, the goal is to isolate the variable by performing the inverse operation (division or multiplication) to both sides of the equation. For example, to solve the equation $3x = 15$, you would divide both sides by 3 to get $x = 5$, isolating the variable $x$. This process of using inverse operations to isolate the variable is the key to solving one-step equations involving multiplication or division.
• Analyze how the properties of equality and inverse operations are fundamental to solving one-step equations, and explain how this lays the groundwork for solving more complex linear equations.
  • The properties of equality, which state that the same operations can be performed on both sides of an equation without changing the equality, are essential to solving one-step equations. By using inverse operations, such as addition and subtraction or multiplication and division, students can isolate the variable and find its value. Mastering this process of solving one-step equations lays a crucial foundation for solving more complex linear equations in the future. The skills of identifying the appropriate inverse operation, applying it to both sides of the equation, and simplifying the resulting expression are all building blocks that enable students to tackle higher-level linear equations involving multiple steps or more advanced algebraic concepts. The ability to fluently solve one-step equations is a fundamental prerequisite for success in more advanced algebra.

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 are used to isolate the variable in an equation.

Solving Equations: Solving an equation means finding the value of the variable that makes the equation true. This is done by using the properties of equality to isolate the variable.