Linear Equation Calculator

Reviewed by CalcMulti Editorial Team·Last updated: March 2026·← Algebra Hub

A linear equation has the form ax + b = c, where the unknown x appears only to the first power. Solving means isolating x: subtract b from both sides, then divide by a. This calculator handles any linear equation in one variable, showing every algebraic step.

Linear equations are the foundation of algebra — they model constant-rate problems, break-even analysis, unit conversions, and any situation where one quantity changes proportionally with another.

The golden rule of solving linear equations: whatever you do to one side, you must do to the other side. Operations that preserve equality include: adding or subtracting the same number, multiplying or dividing by the same non-zero number, and distributing multiplication over addition. Combining like terms and using the distributive property simplify complex-looking equations into the basic ax = b form.

Worked example — solve 3(2x − 4) = 2(x + 5). Distribute: 6x − 12 = 2x + 10. Subtract 2x from both sides: 4x − 12 = 10. Add 12 to both sides: 4x = 22. Divide by 4: x = 5.5. Verification: 3(2(5.5) − 4) = 3(7) = 21 and 2(5.5 + 5) = 2(10.5) = 21 ✓.

Real-world applications: (1) Break-even — a business earns $50 per unit and has $800 fixed costs plus $30 variable cost: 50x = 800 + 30x → x = 40 units. (2) Temperature conversion — Celsius to Fahrenheit: F = 1.8C + 32; solve for C given F = 77 → C = 25°. (3) Loan interest — total = principal + rate × time: 1300 = 1000 + r(3000) → r = 10%. Any time two quantities are related by a constant rate, a linear equation describes the relationship.