Algebra Balance Lab
Enter a linear equation and choose an operation to perform on both sides. The lab records each equivalent transformation using exact fractions, shows the two sides on a symbolic balance and checks proposed x values in the original and current equation. Identities have infinitely many solutions; contradictions have none.
Key features
- Exact rational arithmetic for one-variable linear equations, including parentheses, decimals and fractions
- Add or subtract a linear expression from both sides; multiply or divide by a nonzero constant
- Reject zero multiplication or division because those steps can destroy equivalence
- Step history and undo, with a symbolic balance and test-value tilt
- Distinguish one solution, an identity with infinitely many solutions and a contradiction with no solution
- Download a local JSON report with original and current substitution checks
How to use
- Enter an equation such as 2x + 3 = 11, or load one of the three examples.
- Choose add, subtract, multiply or divide and enter the expression or nonzero constant to apply to both sides.
- Watch the exact equation and history update; undo a step if you want to try another route.
- Enter a test value for x to compare both sides in the original and current equation.
- Review the solution classification and download a JSON report if useful.
Use cases
- Practice isolating x by subtracting a term from both sides
- See why multiplying both sides by zero is not a reversible solving step
- Compare an identity such as 2(x+1)=2x+2 with a contradiction such as x+1=x+2
Frequently asked questions
Why does multiplying by zero fail?
Although both sides become zero, this can turn an equation with one or no solution into 0=0. The lab permits only reversible multiplication or division by a nonzero constant.
Can I subtract x from both sides?
Yes. Addition and subtraction accept a linear expression such as x+2. Multiplication and division accept only a nonzero constant, so the equation remains linear and equivalent.
What is the difference between an identity and a contradiction?
An identity simplifies to the same expression on both sides and is true for every x. A contradiction simplifies to unequal constants and has no solution.
Are the results rounded?
No. Finite decimal inputs become exact fractions. Each reduced numerator and denominator is bounded to 10^18, and input/step limits prevent runaway calculations.
Does the balance picture measure real weight?
No. It is a symbolic teaching metaphor. Its tilt compares the numeric sides only at the x value you test; the algebra and substitution report are authoritative.
Can it solve quadratic or arbitrary symbolic equations?
No. It accepts one variable x with +, -, *, / and parentheses only where the result is linear. Powers, functions, variable denominators and nonlinear products are rejected.
Privacy
Equation input, transformation history and test values remain in this browser tab. A JSON file is created only when you press Download. Nothing is automatically uploaded or saved after leaving.
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