What Are One-Step Equations?
A one-step equation is an algebraic equation that can be solved in just one step. These equations involve a single operation — addition, subtraction, multiplication, or division — that you need to “undo” to find the value of the variable. One-step equations are the foundation of algebra and are typically one of the first topics students encounter.
Understanding Inverse Operations
The key to solving one-step equations is using inverse operations. An inverse operation is the opposite of another operation. Here are the pairs:
- Addition and Subtraction are inverses of each other
- Multiplication and Division are inverses of each other
Whatever operation is being done to the variable, you simply do the opposite to both sides of the equation. This isolates the variable and gives you the solution.
Examples
Example 1: Addition Equation
Solve: x + 5 = 12
Since 5 is being added to x, we subtract 5 from both sides:
x + 5 − 5 = 12 − 5 → x = 7
Example 2: Multiplication Equation
Solve: 3x = 18
Since x is being multiplied by 3, we divide both sides by 3:
3x ÷ 3 = 18 ÷ 3 → x = 6
Example 3: Subtraction Equation
Solve: x − 9 = 4
Since 9 is being subtracted from x, we add 9 to both sides:
x − 9 + 9 = 4 + 9 → x = 13
Tips for Success
- Always perform the same operation on both sides of the equation
- Check your answer by plugging it back into the original equation
- Remember: the goal is to get the variable by itself on one side
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