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Algebra

Linear Equations Solver

Solve linear equations with one or more variables step by step. Get instant step-by-step solutions, completely free, no signup required.

Free Linear Equations Solver Calculator

Enter your problem below to get an instant step-by-step solution.

About Linear Equations Solver

Solve linear equations with one or more variables step by step. Algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols. Mastering algebraic techniques is essential for every level of mathematics, from high school through university.

Our Linear Equations Solver calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any linear equations solver expression and receive a complete, verified solution with every step shown.

Linear Equations Solver Formula

ax + b = c → x = (c − b) / a

A linear equation has a variable raised only to the first power, so its graph is a straight line and it has exactly one solution (unless it is an identity or a contradiction). The goal is to isolate the variable by doing the same inverse operation to both sides: undo addition with subtraction, undo multiplication with division.

Worked Example

Solve 3(x − 4) + 5 = 2x + 7

  1. Distribute: 3x − 12 + 5 = 2x + 7
  2. Combine like terms on the left: 3x − 7 = 2x + 7
  3. Subtract 2x from both sides: x − 7 = 7
  4. Add 7 to both sides: x = 14
  5. Check: 3(14 − 4) + 5 = 35 and 2(14) + 7 = 35 ✓

Answer: x = 14

Common Mistakes to Avoid

  • Distributing a negative sign to only the first term inside the brackets.
  • Moving a term across the equals sign without changing its sign.
  • Dividing only one term by the coefficient instead of the whole side.

How to Use the Linear Equations Solver Calculator

  1. 1

    Type your Linear Equations Solver problem into the input field above

  2. 2

    Press Enter or click the Solve button to run the calculation

  3. 3

    Review the step-by-step solution that appears below the input

  4. 4

    Check the breakdown of each operation to understand the method

  5. 5

    Try a different problem to practice and build your understanding

Frequently Asked Questions

What is the Linear Equations Solver formula?

ax + b = c → x = (c − b) / a. A linear equation has a variable raised only to the first power, so its graph is a straight line and it has exactly one solution (unless it is an identity or a contradiction). The goal is to isolate the variable by doing the same inverse operation to both sides: undo addition with subtraction, undo multiplication with division.

Can you show a worked Linear Equations Solver example?

Solve 3(x − 4) + 5 = 2x + 7: Distribute: 3x − 12 + 5 = 2x + 7; Combine like terms on the left: 3x − 7 = 2x + 7; Subtract 2x from both sides: x − 7 = 7; Add 7 to both sides: x = 14; Check: 3(14 − 4) + 5 = 35 and 2(14) + 7 = 35 ✓. Answer: x = 14.

Is this Linear Equations Solver calculator free to use?

Yes, the Linear Equations Solver calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.

Can I use this for Linear Equations Solver homework and exam practice?

Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.

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