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Linear Equation Solver — Solve ax+b=c

Solve linear equations in one variable (ax + b = c) with step-by-step solutions.

Solve ax + b = c

What Is the Linear Equation Solver — Solve ax+b=c?

The Linear Equation Solver finds the value of x in a one-variable linear equation of the form ax + b = c. Linear equations are the simplest type of equation and are the building block of algebra. The solution is found by isolating x through inverse operations (addition/subtraction and multiplication/division).

Formula

Standard form: ax + b = c Solution: x = (c − b) / a (when a ≠ 0) Steps: 1. Subtract b from both sides: ax = c − b 2. Divide both sides by a: x = (c − b) / a Special cases: a = 0, b ≠ c → No solution (contradiction) a = 0, b = c → Infinitely many solutions (identity)

How to Use

Enter the coefficients a, b, and c for the equation ax + b = c. Click Solve to see the step-by-step working and the solution for x. The tool handles all cases including no solution and infinite solutions.

Example Calculation

Solve 3x + 7 = 22 a=3, b=7, c=22 Step 1: 3x = 22 − 7 = 15 Step 2: x = 15/3 = 5 Verification: 3(5) + 7 = 15 + 7 = 22 ✓

Understanding Linear Equation — Solve ax+b=c

Linear equations are the foundation of algebra and appear in almost every field: calculating costs (fixed cost + variable cost = budget), distance-rate-time problems, mixing solutions, and break-even analysis in business.

The technique of "balancing" both sides of an equation — doing the same operation to both sides — is fundamental to all of algebra. This balance principle extends to inequalities, systems of equations, and matrix equations.

In physics, many fundamental laws are expressed as linear equations: Ohm's Law (V = IR), Hooke's Law (F = kx), and Newton's First Law in constant velocity scenarios. Mastering the one-variable linear equation is the gateway to understanding these laws.

Frequently Asked Questions

What makes an equation "linear"?

A linear equation has the variable raised only to the first power (no x², x³, etc.) and the variable does not appear inside a function like sin(x) or log(x). Its graph is always a straight line.

What happens when a = 0?

If a = 0, the equation becomes b = c. If b ≠ c, there is no solution (contradiction). If b = c, then any x satisfies it, so there are infinitely many solutions.

How do I handle equations like 2(x+3) = 14?

First expand: 2x + 6 = 14, so a=2, b=6, c=14. The tool solves the standard form ax + b = c, so expand brackets before entering values.

Can I solve for variables other than x?

The solver always finds the value of x. To solve for a different variable, simply substitute that variable in place of x in your equation.

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