Equation Solver

Solve a linear equation for x and see the algebra steps, including equations with decimals, division, parentheses, or variables on both sides.

Quick AnswerEnter one linear equation, such as 2x + 5 = 17, then select Solve Equation. The solver simplifies both sides, gathers the x terms, and isolates x. For the example, 2x = 12, so x = 6.

Supported: numbers, x, decimals, parentheses, +, −, ×, ÷, and one equals sign.

Solution
x = 6

One real solution

Steps

  1. Simplify both sides: 2x + 5 = 17.
  2. Move constants: 2x = 12.
  3. Divide by 2: x = 6.
  4. Check: 2(6) + 5 = 17.

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How to Use This Equation Solver

Type a complete equation with an expression on each side of the equals sign. Use x as the variable. You may enter multiplication explicitly, as in 3*(x−2)=12, or use common implicit multiplication, as in 3(x−2)=12 or 2x+5=17.

  1. Enter a one-variable linear equation.
  2. Select Solve Equation or press Enter.
  3. Read the solution classification and algebra steps.
  4. Check the answer by substituting it into the original equation.

This linear equation solver accepts decimals and constant denominators, such as x/4+2=5. It intentionally rejects x², x · x, variables in denominators, and other nonlinear forms. Use the Quadratic Formula Calculator for equations with an x² term. For two linear equations in x and y, use the System of Equations Solver.

How Solving a Linear Equation Works

A linear equation in one variable can be reduced to the form ax + b = cx + d. The goal is to collect variable terms on one side and constants on the other without changing the equality.

ax + b = cx + d ⟹ (a − c)x = d − b ⟹ x = d − ba − c

Each legal operation must affect both sides equally. You may add or subtract the same value from both sides. You may also multiply or divide both sides by the same nonzero value. These properties keep the equation balanced.

The calculator parses each side as a linear expression ax + b. It combines like terms, subtracts the right-side x coefficient from the left-side coefficient, and subtracts the left constant from the right constant. When the final x coefficient is nonzero, division gives one solution.

Equation Solver Examples

Example 1: x on one side

Solve 2x + 5 = 17. Subtract 5 from both sides to obtain 2x = 12. Divide both sides by 2, giving x = 6. Substitute 6 into the original equation: 2(6) + 5 = 17, so the answer checks.

Example 2: parentheses

Solve 3(x − 2) = 12. Distribute 3 to get 3x − 6 = 12. Add 6 to both sides, producing 3x = 18. Divide by 3, so x = 6.

Example 3: variables on both sides

Solve 2x + 3 = x − 4. Subtract x from both sides: x + 3 = −4. Subtract 3 from both sides: x = −7. Checking gives −11 = −11.

One Solution, No Solution, or Infinitely Many Solutions

Reduced form Result Example
ax = b, a ≠ 0 One solution 2x = 12 ⇒ x = 6
0x = b, b ≠ 0 No solution 2x + 2 = 2x + 3
0x = 0 Infinitely many solutions 2(x + 1) = 2x + 2

A contradiction such as 0 = 1 means no value of x can satisfy the equation. An identity such as 0 = 0 means every real value of x satisfies it. The output labels these cases instead of attempting to divide by zero.

Common Equation-Solving Mistakes

Changing only one side

An equation is a balance. If you add, subtract, multiply, or divide to isolate x, apply the same operation to both sides.

Missing a distribution term

In 3(x − 2), multiply both x and −2 by 3. The result is 3x − 6, not 3x − 2.

Combining unlike terms

Terms containing x combine with other x terms. Constant numbers combine with constants. For example, 2x + 3x = 5x, but 2x + 3 cannot be simplified to 5x.

Dividing by zero

The division property requires a nonzero divisor. When the x coefficient cancels to zero, classify the equation as an identity or contradiction instead.

Skipping the check

Substitute the answer into the original equation. If the left and right sides match, the solution is verified.

Equation Solver FAQs

What equations can this solver handle?

It handles one-variable linear equations in x, including decimals, constant division, parentheses, and variables on both sides.

Can it solve for x step by step?

Yes. It reduces the equation to a coefficient times x equals a constant, divides to isolate x, and checks unique solutions.

Can I enter 2x instead of 2*x?

Yes. Both explicit and implicit multiplication are accepted for common linear forms.

What does no solution mean?

It means simplifying the equation produces a false statement, such as 0 = 1. No real number can make the original equation true.

What do infinitely many solutions mean?

It means both sides are equivalent expressions. Every real value of x makes the equation true.

Does the equation solver support fractions?

You may use division by a constant, such as x/4. A variable in the denominator is not supported because it makes the expression nonlinear.

Does this calculator solve quadratic equations?

No. This page is scoped to linear equations. Quadratic equations contain an x² term and require a different solving method.

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Reviewed by Prof. Dr. Khalil Mudassar (PhD)

Sources

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Disclaimer

This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.