Solving One-Step Equations
Learn to solve equations that require just one operation to find the unknown value.
Definition
- Addition and subtraction are opposites:
- Multiplication and division are opposites:
Try it now
Worked Examples
Solve:
Identify what's happening to
has added to it → Operation: addition
Use the inverse operation
The inverse of addition is subtraction → Subtract from both sides
Subtract from both sides
→
Check your answer
✓ → Correct!
Answer:
Common Mistakes
Using the same operation instead of the inverse
Why it's wrong: Students sometimes add when they should subtract, or multiply when they should divide.
Correct: Remember: to undo addition, subtract. To undo subtraction, add. To undo multiplication, divide. To undo division, multiply.
Only applying the operation to one side
Why it's wrong: The equation becomes unbalanced and the solution is wrong.
Correct: Always do the same thing to BOTH sides of the equation. Think of a balance scale!
Forgetting to check the answer
Why it's wrong: Without checking, you might not catch arithmetic errors.
Correct: Always substitute your answer back into the original equation to verify.
Confusing with
Why it's wrong: means (multiplication), while is addition.
Correct: needs division: . But needs subtraction: .
Interactive Visual
Balance Scale
Solution: x = 4
Equation Solver
Ready to solve some equations?
Follow along as we solve the equation step by step.
Interactive Sandbox
Expression Calculator
Try these:
History
No calculations yet
Practice Problems
18 problemsSolve:
Why It Matters
- Shopping: If you have 25 dollars and need 40 dollars for a game, how much more do you need? ()
- Cooking: A recipe serves 4 people but you need to serve 12. How many times do you multiply the recipe? ()
- Sports: A player scored some points in the first half and 15 in the second half for a total of 32. First half points? ()
- Sharing: 5 friends share a prize equally and each gets 8 euros. What was the total prize? ()
Real World Applications
Shopping Budget
Calculating how much you can spend or need to save.
Example:
You want to buy a book that costs 18 euros. You have 11 euros. How much more do you need? Equation: , so euros.
A video game costs 45 euros. After your birthday, you have some money. You need 17 more euros to buy the game.
How much birthday money did you receive?
Step 1: Write the mathematical expression
Write the equation:
Recipe Scaling
Adjusting recipes for different numbers of servings.
Example:
A recipe makes 6 cookies per batch. You need 42 cookies for a party. How many batches? Equation: , so batches.
Each pizza serves 3 people. You need to feed 24 guests at a party.
How many pizzas should you order?
Step 1: Write the mathematical expression
Write the equation:
Sports Statistics
Finding unknown scores or statistics in games.
Example:
A basketball player scored 23 points total. She made 8 points from free throws. How many points were from field goals? Equation: , so points.
A team scored 4 goals in the second half. Their total for the game was 7 goals.
How many goals did they score in the first half?
Step 1: Write the mathematical expression
Write the equation:
Key Takeaways
- 1A one-step equation can be solved with exactly one inverse operation
- 2Addition and subtraction are inverse operations
- 3Multiplication and division are inverse operations
- 4Always perform the same operation on BOTH sides of the equation
- 5Check your answer by substituting it back into the original equation
Frequently Asked Questions
Glossary
- Equation
- A mathematical statement showing that two expressions are equal, using an equals sign ()
- Variable
- A letter (like , , or ) that represents an unknown number
- Inverse operation
- An operation that undoes another operation (addition/subtraction, multiplication/division)
- Isolate
- To get a variable alone on one side of the equation
- Solution
- The value that makes the equation true when substituted for the variable