Find Value Calculator
Linear Equation Solver works out Solution and Solution as a fraction from Input style, Equation and Variable. The default figures on this page give solution of -12; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
5 steps
- Start: 3x + 5 = 2x - 7
- Move every term to the left: (3x + 5) - (2x - 7) = 0, which collects to x + 12 = 0.
- Isolate x: 1x = -12.
- Divide both sides by 1: x = -12 / 1 = -12.
- Check: left side = -31, right side = -31.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Linear Equation Solver calculates
Solves a linear equation in one variable, showing the collection of like terms, the isolation step and the substitution check.
How to use this Linear Equation Solver
Enter Input style, Equation, Variable and a (coefficient of the variable on the left). Solution updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Solution, Solution as a fraction and Answer.
The method follows OpenStax, Elementary Algebra 2e, Chapter 2: Solving Linear Equations and Inequalities and Paul Dawkins, Paul’s Online Notes, Algebra – Linear Equations.
3x + 5 = 2x - 7 example
With Equation: 3x + 5 = 2x - 7, the calculator returns Solution: -12, Left side at the solution: -31, Right side at the solution: -31. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Solution, Solution as a fraction and Answer. The inputs you can vary are Input style, Equation, Variable, a (coefficient of the variable on the left), b (constant on the left) and c (coefficient of the variable on the right).
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do I calculate the z value?
Solves a linear equation in one variable, showing the collection of like terms, the isolation step and the substitution check. Open “How this is worked out” beside the result to see each step for your own figures.
How to get z value in calculator?
It needs Input style, Equation, Variable, a (coefficient of the variable on the left), b (constant on the left) and c (coefficient of the variable on the right). Nothing else is required, and the figures stay in your browser.
What information do I need for the Linear Equation Solver?
You need Input style, Equation, Variable, a (coefficient of the variable on the left), b (constant on the left), c (coefficient of the variable on the right) and d (constant on the right). The page opens with default figures that give solution of -12, so you can see the scale before entering your own.
What does this Linear Equation Solver show?
It shows Solution, Solution as a fraction, Answer, Type of equation, Collected form, Net coefficient of the variable, Net constant term and Left side at the solution, with the working and any warnings for your entries.
Can I check how the Linear Equation Solver result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.