Balance Algebra — Solve for x on a Balance Scale (Free Game)

Balance Algebra is a free game that teaches solving equations with a balance scale. Each purple box on the scale hides the same mystery number, x. Gold blocks are weights, and red balloons stand for negative numbers. Your job is to get one box alone on a pan by doing the same thing to both sides, so the scale stays level. Then you check your answer by putting it back into the original equation. There are 30 puzzles in five worlds, plus random practice and a mode for your own equations. No account is needed.

How to play

1. Pick a puzzle from the map, or press Play puzzle to continue where you left off.
2. Choose a move: Take away, Add, or Split into groups. Then choose how many, and whether you are moving weights or x-boxes.
3. Press the big button to apply the move to both sides. The equation above the scale updates after every step, and the step list underneath records your path. For example, 3x + 2 = 14 becomes 3x = 12, then x = 4.
4. Shortcut: tap a weight, balloon or box on the scale and the game sets up the matching move for you. You still press the button to do it.
5. When one box is alone, press Check it!. The boxes open to show the value, and the game substitutes it into the original equation to show that both sides are equal.

Each puzzle has a par, the fewest steps that solve it. Matching par earns 3 stars, going over by one or two steps earns 2, and a longer path earns 1. A Hint tells you the next standard move and limits that puzzle to 2 stars. You can Undo a step or Restart at any time, and stars and unlocked puzzles are saved in your browser.

The five worlds

• World 1 · Take Away: equations like x + 3 = 7 and 12 = x + 8. Remove weights to leave the box alone.
• World 2 · Split Into Groups: equations like 3x = 12. Share the weights equally, one group for each box.
• World 3 · Two Steps: equations like 3x + 2 = 14. Take away first, then split.
• World 4 · Boxes on Both Sides: equations like 3x + 2 = x + 10. Remove boxes from one pan first.
• World 5 · Balloons & Negatives: equations like 2x − 4 = 10 and x + 9 = 4. Each balloon is −1 and pulls its pan up. Adding a weight cancels a balloon, and some answers are negative.

Each world has six puzzles, and finishing one puzzle unlocks the next. Practice deals a random equation from any world. Build your own equation lets you type in an equation of the form ax + b = cx + d, such as one from homework. The game accepts it only when x is a whole number.

Why the balance model works

An equation says that two amounts are equal, and a level scale shows the same thing. If you take 2 off only one pan, the scale tips and the two sides are no longer equal. The game shows this when you press Left pan only or Right pan only. The scale tips, the move is not counted, and the scale goes back to level. Doing the same thing to both sides is the rule behind every step of solving an equation.

Splitting into groups shows what division does. With 3 boxes and 12 weights, you can split each pan into 3 equal groups, and one box balances one group of 4. If a pan can’t be split evenly, the game explains why and lets you choose a different number.

From pictures to symbols

The picture and the written equation are always shown side by side, so every move links an action on the scale to a line of algebra. Once you are comfortable, switch to Symbols only to hide the scale and solve from the equation alone, as on a test. The moves, par and stars work the same way, and you can switch back whenever you like.

Tips for students preparing for tests

• Use the same order every time: remove x from one side, then remove the plain number next to the x, then divide.
• Always substitute your answer into the original equation. It takes a few seconds and catches most mistakes on multiple-choice questions.
• For a negative number next to x, such as 2x − 4 = 10, add 4 to both sides instead of subtracting.
• Try a World 4 or 5 puzzle in Symbols only mode, then turn the scale back on to check your thinking.

FAQ

What grade is this for? Worlds 1–3 suit upper elementary and middle school students starting algebra. Worlds 4–5 cover the one-variable equations in Algebra 1 and on tests like the SAT, ACT and GED.

Why did I get 2 stars when I matched par? Using a hint limits a puzzle to 2 stars. Replay it without a hint to earn 3.

Can I save my progress? Yes. Stars, unlocked puzzles and stickers are saved in your browser on this device.