One-Step Equation Calculator
Solve simple one-step equations using inverse operations
Examples: x + 5 = 12, x - 3 = 7, 4x = 20, x/2 = 6
Understanding One-Step Equations
A one-step equation is the simplest type of linear equation that can be solved in just one step using inverse operations. These equations involve a single operation applied to the variable.
Four Types of One-Step Equations
1. Addition: x + a = b
Use subtraction to solve
Example: x + 5 = 12 → x = 12 - 5 → x = 7
2. Subtraction: x - a = b
Use addition to solve
Example: x - 3 = 7 → x = 7 + 3 → x = 10
3. Multiplication: ax = b
Use division to solve
Example: 4x = 20 → x = 20 ÷ 4 → x = 5
4. Division: x/a = b
Use multiplication to solve
Example: x/2 = 6 → x = 6 × 2 → x = 12
Inverse Operations
Inverse operations are operations that "undo" each other. To solve one-step equations, we use the inverse operation to isolate the variable:
- Addition ↔ Subtraction
- Multiplication ↔ Division
Frequently Asked Questions
What is a one-step equation?
A one-step equation is an equation that can be solved using just one inverse operation. It contains a variable and one mathematical operation (addition, subtraction, multiplication, or division).
What are inverse operations?
Inverse operations are pairs of operations that undo each other. Addition and subtraction are inverses, as are multiplication and division. We use inverse operations to isolate the variable.
How do I know which inverse operation to use?
Look at the operation being applied to the variable. If the variable is being added to, use subtraction. If it's being multiplied by a number, use division. The goal is to get the variable by itself.
Why do we perform the same operation on both sides?
To keep the equation balanced, whatever you do to one side must be done to the other. This maintains the equality. Think of it like a balanced scale - if you add weight to one side, you must add the same weight to the other.
Can one-step equations have negative solutions?
Yes, one-step equations can have negative, positive, zero, or fractional solutions. The type of solution depends on the numbers in the equation.
How do I check my answer?
Substitute your answer back into the original equation. If both sides equal the same value, your answer is correct. For example, if x = 7 in x + 5 = 12, check: 7 + 5 = 12 ✓
What's the difference between one-step and two-step equations?
One-step equations require only one inverse operation to solve, while two-step equations require two operations. For example, x + 5 = 12 is one-step, but 2x + 5 = 12 is two-step.
Are one-step equations important for learning algebra?
Yes, one-step equations are fundamental to algebra. They teach the basic concept of using inverse operations to isolate variables, which is essential for solving more complex equations.