Solving One-Step Equations

Learn to solve equations that require just one operation to find the unknown value.

Intermediate25 minLesson
Printable worksheet

Definition

A one-step equation is an equation that can be solved in exactly one step using an inverse (opposite) operation.
The goal is to isolate the variable (get it alone on one side).
Inverse Operations:
  • Addition and subtraction are opposites: x+5=12⇒x=12−5x + 5 = 12 \Rightarrow x = 12 - 5
  • Multiplication and division are opposites: 4x=20⇒x=20÷44x = 20 \Rightarrow x = 20 \div 4
The Balance Principle: Whatever you do to one side of the equation, you must do to the other side to keep it balanced:
x+5=12x + 5 = 12
x+5−5=12−5x + 5 - 5 = 12 - 5
x=7x = 7

Try it now

Solve: x+5=12x + 5 = 12

Worked Examples

Solve: x+7=15x + 7 = 15
1

Identify what's happening to xx

xx has 77 added to it → Operation: addition
2

Use the inverse operation

The inverse of addition is subtraction → Subtract 77 from both sides
3

Subtract 77 from both sides

x+7−7=15−7x + 7 - 7 = 15 - 7 → x=8x = 8
4

Check your answer

8+7=158 + 7 = 15 ✓ → Correct!

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 3x3x with x+3x + 3

Why it's wrong: 3x3x means 3×x3 \times x (multiplication), while x+3x + 3 is addition.

Correct: 3x=153x = 15 needs division: x=5x = 5. But x+3=15x + 3 = 15 needs subtraction: x=12x = 12.

Interactive Visual

Balance Scale

x + 7=15
x
7
15
Apply to both sides:

Solution: x = 8

Equation Solver

Solve for xx:

x+7=15x + 7 = 15
1
x+7=15x + 7 = 15
Subtract 77 from both sidesRemove the constant term

Tips:

  • • Whatever you do to one side, do to the other
  • • Undo operations in reverse order (PEMDAS backwards)
  • • Check your answer by substituting back

Follow along as we solve the equation step by step.

Interactive Sandbox

Expression Calculator

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Practice Problems

18 problems
Problem 1 of 18
Easy
Solve: x+5=12x + 5 = 12

Why It Matters

One-step equations are the foundation of all algebra. Once you master them, you have the key tool for every harder equation that comes later.
Real-life applications:
  • Shopping: If you have 25 dollars and need 40 dollars for a game, how much more do you need? (x+25=40x + 25 = 40)
  • Cooking: A recipe serves 4 people but you need to serve 12. How many times do you multiply the recipe? (4x=124x = 12)
  • Sports: A player scored some points in the first half and 15 in the second half for a total of 32. First half points? (x+15=32x + 15 = 32)
  • Sharing: 5 friends share a prize equally and each gets 8 dollars. What was the total prize? (x5=8\frac{x}{5} = 8)

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 dollars. You have 11 dollars. How much more do you need? Equation: 11+x=1811 + x = 18, so x=7x = 7 dollars.

1Try It Yourself

A video game costs 45 dollars. The only money you have is what you got for your birthday, and you still need 17 dollars more to buy the game.

How much birthday money did you receive?

Step 1: Write the mathematical expression

From x+17=45x + 17 = 45, write the calculation that gives xx:

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: 6b=426b = 42, so b=7b = 7 batches.

2Try It Yourself

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

From 3p=243p = 24, write the calculation that gives pp:

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: x+8=23x + 8 = 23, so x=15x = 15 points.

3Try It Yourself

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

From g+4=7g + 4 = 7, write the calculation that gives gg:

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

Look at what's being done to the variable and do the opposite. If the variable has something added to it, subtract. If multiplied, divide. And vice versa.
Look at what's being done to the variable and do the opposite. If the variable has something added to it, subtract. If multiplied, divide. And vice versa.
An equation is like a balance scale. If you add weight to one side, you must add the same weight to the other side to keep it balanced. The same applies to equations.
The process is the same! For example, in 15=x+715 = x + 7, subtract 77 from both sides to get 8=x8 = x, which is the same as x=8x = 8.

Glossary

Equation
A mathematical statement showing that two expressions are equal, using an equals sign (==)
Variable
A letter (like xx, yy, or nn) 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
Today's challengeOne problem, three tries

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