Two-Step Equations
Undo addition or subtraction first, then multiplication or division.
About this topic
A two-step equation has the variable involved in two operations, such as 3x + 4 = 19. Solve it by undoing them in reverse order of the order of operations: first remove the addition or subtraction, then the multiplication or division. Here subtract 4 to get 3x = 15, then divide by 3 to get x = 5.
Keep the equation balanced at every step and write each step on a new line. These equations model everyday situations like a fixed fee plus a per-item cost. Think of unwrapping a present: the last thing put on is the first thing taken off. With x/2 − 3 = 5, add 3 to get x/2 = 8, then multiply by 2 to find x = 16.
Suppose a gym charges a 20 dollar joining fee plus 15 dollars a month, and you have paid 110 dollars. Then 15m + 20 = 110, so 15m = 90 and m = 6 months. Checking: 15 × 6 + 20 = 110, which is correct. Phone plans, taxi fares and savings goals produce equations of this form.
The most common error is dividing first without dividing every term: in 3x + 4 = 19, dividing by 3 would require 4/3 and 19/3, which is messy and error-prone. Subtracting first is cleaner. Another is forgetting the negative: in 5 − 2x = 1, subtract 5 to get −2x = −4, so x = 2. Always substitute to check.
Key ideas
- Reverse the order of operations
- Keep both sides balanced
- Always verify the answer
Quick check
Use cases: where Two-Step Equations helps
- Homework: review the key idea behind Two-Step Equations before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Two-Step Equations without notes.
- Visual learning: play with the interactive lab to see how Two-Step Equations changes when you adjust its inputs.
- Teaching a friend: explain Two-Step Equations in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Two-Step Equations?
Undo addition or subtraction first, then multiplication or division.
What will I learn in Two-Step Equations?
Reverse the order of operations. Keep both sides balanced. Always verify the answer.
Is Two-Step Equations part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Two-Step Equations lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Two-Step Equations?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.