What it does
An equation is a balance. The left side and the right side weigh the same, and the job is to find the hidden weight of one box, x. On this page each x box is a blue square and each 1-weight is a small orange disc. The equation 3x + 5 = x + 13 is three boxes and five weights on the left pan, one box and thirteen weights on the right.
You solve it the way you would with a real balance: whatever you do, do it to both pans, so the beam stays level.
- − 1 from each or − all 1s you can: lift the same weights off both pans.
- − x from each: lift a box off both pans.
- Share into … groups: split both pans into equal groups and keep one group (this is dividing both sides).
- Swap pans: x = 4 is the same as 4 = x.
When a single box sits alone opposite some weights, you have solved it. A guess slider shows what happens when you try a value: the beam tips towards the heavier pan, and it is level only at the answer.
It follows the Class 8 maths chapter Algebra Play. Number tricks that lead to the same algebra are in number trick decoder, and two equations at once are in linear pairs.
How to use it
- Type the equation in the four boxes: x’s and 1s on the left, x’s and 1s on the right. Or press New equation.
- Press the move buttons. Each move is written in the list under the scale with the new equation.
- Stuck? Press Hint. Made a mess? Start again.
- Move the x slider (or type a value) to test a guess. The text shows what each pan weighs.
A worked example
Start with 3x + 5 = x + 13.
- − x from each: 2x + 5 = 13.
- − all 1s you can (5 from each): 2x = 8.
- Share into 2 groups: x = 4.
Check with the slider at x = 4: the left pan weighs 3 × 4 + 5 = 17, the right pan 4 + 13 = 17. Level. At x = 2 the left pan weighs 11 and the right 15, so the beam tips right and the page says “Too small”.
Tips
- Take the boxes off first, until only one pan has boxes. Then take the loose weights off that pan. Then share.
- If the boxes can’t be shared evenly (3x = 7), the answer is a fraction: x = 7/3. The page tells you when this happens.
- 2x + 4 = 2x + 4 balances for every x; 2x + 4 = 2x + 6 never balances. Both happen when the boxes cancel completely.
- This picture only shows positive amounts. Equations with minus signs work the same way on paper: add the same to both sides.
Check yourself
Four fresh questions each time: two equations to solve, one with a fraction answer, and a check of a guess. Nothing is saved.
FAQ
Why can’t I take 1 off when one pan is empty? Then you would take from only one side, and the balance (the equation) would no longer be true.
Is this the NCERT book? No. It covers the same topic with fibub’s own pictures and questions. fibub is not part of NCERT.
Where the numbers come from
- Solving linear equations by doing the same operation to both sides is standard school algebra. The pictures, equations and questions were written for fibub.
- Checked against Python's fractions.Fraction for every equation with 0 to 9 boxes and 0 to 30 weights on each side (solution, no solution, or every x).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.