Math / Algebra

Multi-Step Equation Calculator

Solve one-variable linear equations with clear distribution, combining, and isolation steps.

Linear equationsStepsFractionsParentheses

Algebra worksheet

Inputs

Enter your equation

Use x as the variable. Fractions, decimals, parentheses, and implicit multiplication are accepted.

This tool solves first-degree equations in one variable. It does not turn quadratic or rational equations into linear problems.

Result

Answer

x = 6

Status

One solution

The coefficient of x is nonzero, so division leaves one value of x.

Solution steps

  1. 1

    Rewrite both sides

    2x + 6 = 18

    Expand parentheses and write equivalent polynomial expressions on each side.

  2. 2

    Combine like terms

    2x = 12

    Collect the x terms on one side and the constant terms on the other side.

  3. 3

    Divide by the coefficient

    x = 6

    Divide both sides by the nonzero coefficient of x to isolate the variable.

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About this calculator

Method, formulas, and limits.

What this does

Solves one-variable linear equations with constants, decimals, fractions, parentheses, and implicit multiplication, then shows the algebraic steps used to isolate x.

Who it is for

Students checking algebra homework, teachers preparing examples, and anyone who wants to see why a linear equation has one solution, no solution, or infinitely many solutions.

How it works

Both sides are parsed as polynomials, like terms are combined, constants are moved to the opposite side, and the remaining coefficient is divided to isolate x. The parser does not silently turn nonlinear equations into linear ones.

Limitations

This release solves first-degree equations in one variable only. It does not solve systems, inequalities, quadratic equations, or expressions with a variable in a denominator.

Key calculations

Distributive Property
a(b + c) = ab + ac. Expand parentheses before collecting like terms.
Collect Like Terms
Move variable terms together and constants together: ax + b = c becomes ax = c − b.
Isolate the Variable
Divide both sides by the nonzero coefficient: ax = d becomes x = d/a.

Reference ranges

One Solution
Any equation that leaves a nonzero coefficient on x has one solution, such as 3x + 2 = 14.
Infinite Solutions
Equivalent sides reduce to 0 = 0, such as 2(x + 1) = 2x + 2. Every real x satisfies the equation.
No Solution
Equal variable terms but different constants reduce to a false statement such as 0 = 3.

How to use it

  1. 1.Enter one equationType an equation such as 2(x + 3) = 18, x/2 + 3 = 7, or 5x − 4 = 2x + 8.
  2. 2.Review the normalized equationThe calculator expands parentheses and combines like terms without changing the solution.
  3. 3.Follow each isolation stepRead the collected equation and the final division step to see how x is isolated.
  4. 4.Check special casesAn identity means every real number works; a contradiction means no value of x works.

It is an equation that takes more than one operation to solve. You may need to distribute, combine like terms, move constants, and divide by the coefficient of x.

Yes. Use ordinary fractions such as 3/4 and decimal coefficients such as 0.5. Division by an expression containing x is not supported.

After simplification, the variable terms cancel but the constants disagree. A statement such as 0 = 3 is false for every value of x, so there is no solution.

Both sides simplify to the same expression, such as 0 = 0. Every real value of x satisfies the equation.

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