Simple Equation Generator
Builds a sheet of linear equations at the level you ask for. Every solution is a whole number, and every question is checked by substituting the answer back in — which is the same check a pupil is told to do. Every question is computed and checked directly — not a fabricated or AI-guessed fact.
What this generator does
Generates linear equations to solve, with answers. Coefficients are chosen so the solution is a whole number, which is deliberate: an equation whose answer is 3.7142857 tests a calculator rather than the method.
How to use this tool
- Choose a level and how many questions you want.
- Press make questions and work through the sheet.
- Show the answers to mark it, or show the working to see which operation was undone at each step.
- Enter a seed word to rebuild the same sheet later.
Worked examples
- A two-step equation, standard level, seed round9
- 8x + 14 = 174 → x = 20: take 14 from both sides to get 8x = 160, then divide both sides by 8.
Common use cases
- Solving-equations practice
- Quick maths warm-ups
- Self-testing before a maths quiz
How this generator works
The solution value is drawn first, and the equation is built around it by applying the level's operations in reverse — adding a constant, multiplying by a coefficient, moving terms to both sides — so the working equation is guaranteed to have that exact whole-number solution. Before the sheet is shown, the solution is substituted back into the printed equation and both sides are confirmed equal.
Randomness and fairness
The solution is drawn first with the browser's cryptographic random number generator and the equation is then built around it. Generating the equation first and solving it would produce awkward answers most of the time, which is exactly what makes a worksheet unusable. A seed word rebuilds the same sheet later while the generator is unchanged; the seed is for reproducibility, not cryptographic strength, so a seeded sheet is deterministic rather than unpredictable.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Solutions are always whole numbers by construction — negative ones included at stretch level — so an equation whose answer is a fraction or an awkward decimal is not produced.
- Only linear equations in one unknown are covered — quadratics and simultaneous equations have their own generators.
- Brackets appear only at the levels that include them, and never nested inside another bracket.
Common mistakes
- Doing something to one side only
- Whatever you do to one side you do to the other. That is the entire method, and every error in it is a version of forgetting this.
- Dividing before collecting terms
- Get all the unknowns on one side and all the numbers on the other before dividing. Dividing early multiplies the number of fractions to handle.
Related generators
- Algebra Substitution Question GeneratorSubstitution questions built to order — one letter, two letters, squares, brackets and division, all evaluating to whole numbers.
- Simultaneous Equations GeneratorPairs of linear equations built backwards from a whole-number solution, with the elimination worked out line by line.
- Linear Inequality GeneratorInequalities to solve, including the ones where dividing by a negative turns the sign round, with the flip tested rather than asserted.
- Order of Operations Question GeneratorBODMAS/PEMDAS questions built so the order genuinely changes the answer, with worked steps.
- Diophantine Equation GeneratorLinear equations in two unknowns over the integers, with the solvability test, a table of the solution family and the smallest non-negative answer.