Learn one-step equations
A one-step equation can be solved with one inverse operation. The goal is to leave the variable alone while keeping both sides balanced.
You will be able to spot a one-step equation, choose the opposite operation, solve it, and check your answer.
The idea in plain English
An equation says that two amounts are equal. Think of it like a balanced scale: the left side and right side have the same value.
The letter stands for a number we do not know. Undo the one operation attached to it. Do the same thing to both sides so the equation stays balanced.
How to recognise this kind of question
- There is an equals sign.
- The variable has only one operation attached to it.
- One opposite operation will leave the variable alone.
Quick decision: One operation on the variable means one opposite operation on both sides.
The method
- Identify the operation attached to the variable.
- Apply the inverse operation to both sides.
- Substitute the solution into the original equation to check it.
Worked examples
x + 7 = 18
- Subtract 7 from both sides.
- x = 18 − 7
Answer: x = 11
−4x = 28
- The variable is multiplied by −4.
- Divide both sides by −4: x = 28 ÷ (−4).
Answer: x = −7
Your turn—with help
y − 9 = 15
Need a hint?
What undoes subtracting 9?
y − 9 + 9 = 15 + 9
Show the answer and steps
- Add 9 to both sides.
- The −9 and +9 cancel, so y = 24.
- Check: 24 − 9 = 15.
Answer: y = 24
Watch out for this mistake
Incorrect: x + 7 = 18, so x = 25
Why it fails: Adding 7 again does not undo the +7 attached to x.
Do this instead: Subtract 7 from both sides: x = 11.
Quick check
Try these without looking. Then open each answer to check your thinking.
a + 6 = 14
Need a hint?
Undo +6 with −6.
Show the answer and steps
- Subtract 6 from both sides: a = 14 − 6.
Answer: a = 8
5m = 35
Need a hint?
The 5 is multiplying m.
Show the answer and steps
- Divide both sides by 5: m = 35 ÷ 5.
Answer: m = 7
n/4 = −3
Need a hint?
Undo dividing by 4 with multiplication.
Show the answer and steps
- Multiply both sides by 4: n = −3 × 4.
Answer: n = −12
Common mistakes
- Changing only one side of the equation.
- Using the same operation instead of its inverse.
- Skipping the substitution check.
Practice tips
- Say the inverse operation aloud before calculating.
- Mix addition and multiplication examples after each skill is secure.