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Math Equation Solver

Part of: Calculators →

Solve a Linear Equation for x

Enter a linear equation containing x. Supported forms: ax + b = c, ax + b = dx + e, n(x ± c) = d.

Examples: 2x+5=11  ·  3x-7=8  ·  2x+5=x+9  ·  4(x+2)=20

Result will appear here

How to Use the Math Equation Solver

  1. Read the input labels carefully — enter the values they describe.
  2. Use the correct units for each field — check the unit labels before entering numbers.
  3. Click Calculate to see your result.
  4. Review the formula or method shown to verify the calculation makes sense.

Math Equation Solver – Instantly Solve Any Linear Equation

Whether you're a student working through algebra homework, a teacher generating worked examples, or a professional checking a quick calculation, our free Math Equation Solver handles linear equations in one variable with clean, step-by-step output. No sign-up, no external tools.

What Is a Linear Equation?

A linear equation is an equation in which the variable (x) appears only to the first power — no x², no x³. It forms a straight line when graphed and has exactly one solution (unless it's a contradiction or identity).

General form: ax + b = cx + d

Supported Equation Forms

How to Use

  1. Type your equation in the input field using x as the variable.
  2. Use standard notation: 2x+5=11 (spaces optional).
  3. Click Solve to get the solution with step-by-step working.
  4. Click Clear to reset. Press Enter to solve without clicking.

Example Walkthrough

Equation: 4(x + 2) = 20

  1. Expand the bracket: 4x + 8 = 20
  2. Subtract 8 from both sides: 4x = 12
  3. Divide both sides by 4: x = 3

Equation: 2x + 5 = x + 9

  1. Subtract x from both sides: x + 5 = 9
  2. Subtract 5 from both sides: x = 4

The Solving Method

The solver uses standard algebraic manipulation:

  1. Expand any parentheses (e.g. 4(x+2) becomes 4x+8).
  2. Collect all x terms on one side, all constants on the other.
  3. Divide both sides by the coefficient of x.
  4. Report special cases: identity (true for all x) or no solution (contradiction).

Input Tips

Frequently Asked Questions

What types of equations are supported?

Linear equations in one variable (x). The solver handles any equation of the form ax + b = cx + d, including parenthesised terms like 4(x + 2) = 20.

What does "identity" mean?

An identity is an equation true for every value of x — for example, 2x + 4 = 2(x + 2). The solver detects this and reports it clearly.

What does "no solution" mean?

A contradiction — for example, 2x + 3 = 2x + 7. No value of x makes both sides equal.

Can I use decimal coefficients?

Yes — e.g. 1.5x + 2 = 5 is supported.

Does it show steps?

Yes — the solver shows the equation entered, any expansion applied, the collected terms, and the final division step before the answer.

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