Algebra Balance Game
Keep both sides equal. Use legal operations to isolate x.
Daily and practice math puzzles
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Controls & saved progress
Tab through Operation, Term and Amount. Enter applies the operation. Amounts can be integers, fractions or decimals. Hint and Undo mark assistance.
Saved progress stays in this browser when available.
Best scores are separate for each level. Hints and Undo mark assistance; assisted rounds do not replace an unaided best.
How to Play Algebra Balance
Your starting equation contains one unknown, x. The goal is to leave x alone on either side of the equals sign. Choose Add, Subtract, Multiply or Divide, enter an amount, then apply the operation to both sides. For addition or subtraction, choose Number to change the constants or x term to change the coefficients of x. For multiplication and division, use a nonzero number.
The board combines like terms after each step. You may use an integer, a fraction such as 1/2, or a decimal with up to three places. Fractions stay exact, including negative values. The game rejects division by zero, multiplying by zero, multiplying by x and an unchanged equation, because those choices either change the solution set or do not advance this task.
Easy starts with positive values and x on the left. Normal introduces x on both sides and signed constants. Hard can use negative coefficients and fractional solutions. There is no countdown. Aim for a clear sequence of inverse operations, then explain why each step preserves equality.
Worked Example: Collect Terms, Then Isolate x
Start with 3x + 6 = x + 14. Subtract 1x from both sides to get 2x + 6 = 14. Subtract 6 from both sides to get 2x = 8. Divide both sides by 2, giving x = 4. Substitution checks the result: 3 × 4 + 6 = 4 + 14, so both sides equal 18.
You can make another valid sequence. For example, subtracting 6 before collecting x terms also preserves the equation. The game accepts an isolated x on either side and checks the original equation with exact arithmetic. A hint proposes a useful next operation; it does not automatically execute it.
Open Equation steps to review the operations you performed. Undo restores the preceding equation and marks assistance. If a step creates values outside this compact board’s numeric limits, choose a simpler inverse operation or restart. This is a linear-equation practice game, rather than a solver for arbitrary expressions.
Daily Equations, Keyboard and Personal Records
Choose Daily for a repeatable puzzle for the current UTC date and level. Practice creates another equation through New puzzle. Mode and level keep separate saved puzzles in this browser, so changing a setting can resume its previous board. Daily changes at midnight UTC. Clearing browser data removes the saved puzzles and records.
Tab reaches every control. Choose the operation and term, type the amount and press Enter to apply it. On touch screens, use the same labelled fields and the Apply to both sides button. Hint and Undo mark a round assisted. A new completion adds to the shared math-practice calendar.
The score starts at 100 and rewards a short valid solution sequence. Hints reduce the displayed score, and assisted rounds do not replace a best score. Best scores are separate for each level and are personal practice feedback. Only the first completion of the same puzzle adds another solved record.
Frequently Asked Questions
Can the answer be a fraction?
Yes. Hard can have fractional solutions, and exact fractions are accepted as operation amounts. The completed answer is checked in the original equation.
Why can I not multiply both sides by zero?
That would collapse the equation and change its solution set. This game permits only nonzero scaling operations.