Solving One-Step Equations (Addition & Subtraction)

How to solve one-step equations?
Solving one-step equations involves isolating the variable (the letter representing the unknown value) on one side of the equation. Since it’s a “one-step” equation, you’ll only need to perform one operation to achieve this. The key principle is to use inverse operations to undo whatever operation is being applied to the variable.

1. Locate the variable and see what operation is happening to it. (+, -, ×, or ÷)
2. Perform inverse operation to both sides of the equation.
3. Simplify and check you answer.

The following diagram some examples of solving one-step equations. Scroll down the page for more examples and solutions.

 

Algebra Worksheets
Practice your skills with the following Algebra worksheets:
Printable & Online Algebra Worksheets

There are four basic types of one-step equations:

1. Addition Equations (Variable + Number = Constant)
   Goal: To isolate the variable by undoing the addition.
   Inverse Operation: Subtraction.
   Example:
   x + 5 = 12
   To isolate ‘x’, subtract 5 from both sides of the equation:
   x + 5 - 5 = 12 - 5
   x = 7
   Check your answer: Substitute the value of ‘x’ back into the original equation: 7 + 5 = 12 (This is true, so your answer is correct).

2. Subtraction Equations (Variable - Number = Constant)
   Goal: To isolate the variable by undoing the subtraction.
   Inverse Operation: Addition.
   Example:
   y - 3 = 8
   To isolate ‘y’, add 3 to both sides of the equation:
   y - 3 + 3 = 8 + 3
   y = 11
   

3. Multiplication Equations (Number × Variable = Constant)
   Goal: To isolate the variable by undoing the multiplication.
   Inverse Operation: Division.
   Example:
   4z = 20
   To isolate ‘z’, divide both sides of the equation by 4:
   4z / 4 = 20 / 4
   z = 5
   

4. Division Equations (Variable ÷ Number = Constant)
   Goal: To isolate the variable by undoing the division.
   Inverse Operation: Multiplication.
   Example:
   a / 6 = 3
   To isolate ‘a’, multiply both sides of the equation by 6:
   (a / 6) × 6 = 3 × 6
   a = 18

Key Principles to Remember:

• Keep the Equation Balanced: Whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side to maintain the equality. Think of an equation like a balanced scale.
• Use Inverse Operations: To isolate the variable, use the operation that is the opposite of the one being applied to it.
• Check Your Work: Always substitute your solution back into the original equation to verify that it makes the equation true.

Solving 1-step equations (add/subtract)
This video will help you learn by doing: solving 1-step equations using addition and subtraction.

• Show Video

Solving 1-step equations (multiplication/division) Part 1
This lesson covers several kinds of one-step equations that involve multiplication and division, including fractional coefficients.

• Show Video

Solving 1-step equations (multiplication/division) Part 2
Part two of our lesson on solving one-step equations with multiplication and division, including fractional coefficients.

• Show Video

Solving One-Step Addition Equations
Solving an equation for x means isolating the x on one side of the equation.
To isolate the x, the following techniques are used.
If a number is being added to x, subtract the number from both sides of the equation.
If a number is being subtracted from x, add the number to both sides of the equation.
If a number is being multiplied by x, divide both sides of the equation by the number.
If a number is being divided by x, multiply both sides of the equation by the number.

• Show Video

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.