Balance scale – equations step by step
An equation is a balanced scale. Do the same on both sides until only x is left – below the picture you will see every move written in symbols.
Goal: leave just one x on one side of the scale. Then the other side shows how much x weighs.
In symbols:
Steps
You can also click a weight or an x box on the scale – one disappears from each side.
Your moves
How do you play?
On the scale there are x boxes – each weighs the same, but you don’t know how much – and weights of 1. The scale is balanced, so both sides weigh the same. That is an equation (równanie). Your task: leave just one x box on one side. Then the other side shows how much x weighs.
You may only do the same on both sides: remove the same number of weights, remove the same number of x boxes, or divide both sides into the same number of equal parts. Next to the scale there is a list of steps, and the “Hint” button gives first a question, then a concrete move, and finally the number filled in. At the end you check the result: you substitute x into the original equation.
Example: 3x + 2 = 11
Remove 2 weights from both sides: 3x = 9. Divide both sides into 3 equal parts: x = 3. Check: 3 · 3 + 2 = 11. It works.
If x is on both sides, for example 3x + 2 = x + 8: first remove one x from both sides (2x + 2 = 8), then 2 weights (2x = 6), then divide into 2 parts (x = 3).
What is the most common mistake?
Changing only one side. If you take 2 away only on the left of 3x + 2 = 11, the scale tips and the result is wrong. Do every move on both sides – the same in your exercise book: subtract 2 from both sides of the equation.
How does this help in the eighth-grade exam?
In the Polish eighth-grade exam equations usually appear in word problems: you write the relationship as an equation and solve it. In 2025, question 17 had a success rate of 45%, and 32% of pupils gave a full solution. In 2026 a similar question 15 had a success rate of 49%, and just under 38% of pupils solved it without mistakes.
Curriculum: point VI.2 for grades 7–8; in the exam equations come in word problems (point VI.4) (Polish core curriculum, Dz.U. 2024 poz. 996). Sources: CKE report 2025; CKE report 2026 (in Polish).
Questions about the game
Why do we do the same on both sides of an equation?
Because a balanced scale stays balanced only if you take away or add the same on both pans. It is the same with both sides of an equation.
What does a box mean in the game?
A box is the unknown x. All boxes weigh the same, and you have to find their weight.
Is the game free?
Yes. You play in the browser, with no sign-up and no e-mail.
Mini glossary: English – Polish
- equation – równanie
- unknown – niewiadoma
- both sides of the equation – obie strony równania
- solution – rozwiązanie
- check – sprawdzenie
- balance scale – waga
The game runs in your browser. There is no time limit and we save nothing.