Introduction
An equation is a mathematical statement that says two things are equal. Solving an equation means finding the value of the unknown — the letter — that makes that statement true. Single step equations are the simplest type because you only need to perform one operation to find the answer.
They are the foundation of all algebra. Master single step equations and every more complex topic — two step equations, simultaneous equations, quadratic equations — becomes significantly easier.
What Is a Single Step Equation?
A single step equation is an equation that can be solved in exactly one mathematical operation — one addition, one subtraction, one multiplication, or one division.
- x + 5 = 12 (one subtraction needed)
- x − 3 = 8 (one addition needed)
- 3x = 18 (one division needed)
- x ÷ 4 = 5 (one multiplication needed)
The goal is always the same — get the unknown letter on its own on one side of the equation.
The Golden Rule of Equations
Before solving any equation, you must understand and never forget this rule:
Whatever you do to one side of the equation, you must do exactly the same to the other side.
An equation is like a perfectly balanced scale. Both sides are equal. The moment you add, subtract, multiply, or divide on one side without doing the same on the other, the balance is destroyed and your answer will be wrong.
The Four Types of Single Step Equations
Type 1 — Addition Equations
These are equations where a number has been added to the unknown. To solve them, subtract that number from both sides.
x + 7 = 15
To get x on its own, subtract 7 from both sides:
x + 7 − 7 = 15 − 7
x = 8
Check: 8 + 7 = 15 ✓
x + 12 = 30
Subtract 12 from both sides:
x + 12 − 12 = 30 − 12
x = 18
Check: 18 + 12 = 30 ✓
x + 9 = 4
Subtract 9 from both sides:
x + 9 − 9 = 4 − 9
x = −5
Check: −5 + 9 = 4 ✓
Note: the answer can be negative. Do not assume the answer is always a positive number.
Type 2 — Subtraction Equations
These are equations where a number has been subtracted from the unknown. To solve them, add that number to both sides.
x − 6 = 10
Add 6 to both sides:
x − 6 + 6 = 10 + 6
x = 16
Check: 16 − 6 = 10 ✓
x − 15 = 3
Add 15 to both sides:
x − 15 + 15 = 3 + 15
x = 18
Check: 18 − 15 = 3 ✓
x − 4 = −11
Add 4 to both sides:
x − 4 + 4 = −11 + 4
x = −7
Check: −7 − 4 = −11 ✓
Type 3 — Multiplication Equations
These are equations where the unknown has been multiplied by a number. To solve them, divide both sides by that number.
3x = 21
Divide both sides by 3:
3x ÷ 3 = 21 ÷ 3
x = 7
Check: 3 × 7 = 21 ✓
5x = 45
Divide both sides by 5:
5x ÷ 5 = 45 ÷ 5
x = 9
Check: 5 × 9 = 45 ✓
−4x = 20
Divide both sides by −4:
−4x ÷ −4 = 20 ÷ −4
x = −5
Check: −4 × −5 = 20 ✓
Note: when dividing by a negative number, the sign of the answer changes.
Type 4 — Division Equations
These are equations where the unknown has been divided by a number. To solve them, multiply both sides by that number.
x ÷ 3 = 7
Multiply both sides by 3:
x ÷ 3 × 3 = 7 × 3
x = 21
Check: 21 ÷ 3 = 7 ✓
x ÷ 5 = 8
Multiply both sides by 5:
x ÷ 5 × 5 = 8 × 5
x = 40
Check: 40 ÷ 5 = 8 ✓
x/6 = −4
Multiply both sides by 6:
x/6 × 6 = −4 × 6
x = −24
Check: −24 ÷ 6 = −4 ✓
Solving with Fractions
Sometimes the unknown appears with a fractional coefficient. The method is the same — multiply both sides by the denominator to clear the fraction.
x/3 = 5
Multiply both sides by 3:
x = 5 × 3
x = 15
Check: 15 ÷ 3 = 5 ✓
2x/5 = 8
Multiply both sides by 5, then divide by 2:
2x = 8 × 5
2x = 40
x = 40 ÷ 2
x = 20
Check: (2/5) × 20 = 8 ✓
How to Check Your Answer
Always substitute your answer back into the original equation to verify it is correct. If both sides are equal, your answer is right. If they are not equal, you have made an error somewhere and need to recheck your working.
Example: Solve x + 9 = 22
x = 22 − 9 = 13
Check: 13 + 9 = 22 ✓
Frequently Asked Questions
Q1. What is the difference between an equation and an expression?
An expression is a mathematical phrase that contains numbers, variables, and operations but has no equals sign — it cannot be solved, only simplified. An equation has an equals sign and states that two expressions are equal — it can be solved to find the value of the unknown.
- 3x + 5 (expression — no equals sign)
- 3x + 5 = 20 (equation — has an equals sign and can be solved)
Q2. What does it mean to "isolate the variable"?
Isolating the variable means getting the unknown letter completely on its own on one side of the equation. This is the goal of every equation. You do this by performing inverse operations to remove everything around the variable until only the letter remains.
- x + 7 = 15 → subtract 7 from both sides → x = 8
- The variable x is now isolated on the left side.
Q3. Can the answer to an equation be zero or a negative number?
Yes. The answer to an equation can be any number — positive, negative, zero, a fraction, or a decimal. Never assume the answer must be a positive whole number. Always follow the mathematical steps and let the answer reveal itself.
- x + 10 = 10 → x = 0
- x + 15 = 8 → x = −7
- 4x = 6 → x = 1.5
Q4. Why do we always check the answer?
Substituting the answer back into the original equation confirms that both sides are equal and that no arithmetic errors were made during solving. It takes only a few seconds and eliminates the risk of submitting a wrong answer you could have caught yourself.
Q5. What is the difference between a coefficient and a constant?
A coefficient is the number multiplied by the variable. A constant is a standalone number with no variable attached.
- In 5x + 3 = 18: 5 is the coefficient of x, 3 and 18 are constants.
- To solve 5x = 15, divide by the coefficient 5 — not subtract it.