Multi-Step Equations
Simplify each side, collect variables, then isolate.
About this topic
Multi-step equations need extra preparation before the inverse operations. First simplify each side by distributing and combining like terms, then isolate the variable using inverse operations. For 2(x + 3) + x = 15, expand to 3x + 6 = 15, then solve to get x = 3.
Working neatly, line by line, prevents most errors. Some equations have no solution or are true for every value, which you recognise when the variable disappears and you are left with a false or always-true statement. A good routine is: clear fractions by multiplying by the common denominator, distribute, combine like terms, move variable terms to one side and constants to the other, then divide.
Take 3(2x − 1) − 4 = 5x + 2. Expanding gives 6x − 3 − 4 = 5x + 2, so 6x − 7 = 5x + 2. Subtract 5x to get x − 7 = 2, and add 7 to get x = 9. Check: left side 3(17) − 4 = 47, right side 45 + 2 = 47. These skills are used to solve geometry problems like finding a side when perimeter is known, and for balancing budgets.
Typical mistakes include distributing a negative sign incorrectly, such as −(x − 4) becoming −x − 4 instead of −x + 4, and combining unlike terms. Take your time with signs, and always check your solution in the original equation, not a later step.
Key ideas
- Distribute and combine like terms first
- Move variable terms to one side
- Check for no solution or infinite solutions
Quick check
Use cases: where Multi-Step Equations helps
- Homework: review the key idea behind Multi-Step Equations before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Multi-Step Equations without notes.
- Visual learning: play with the interactive lab to see how Multi-Step Equations changes when you adjust its inputs.
- Teaching a friend: explain Multi-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 Multi-Step Equations?
Simplify each side, collect variables, then isolate.
What will I learn in Multi-Step Equations?
Distribute and combine like terms first. Move variable terms to one side. Check for no solution or infinite solutions.
Is Multi-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 Multi-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 Multi-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.