BYTETOOLS

Linear Equation Solver

Solve linear equations like 3x + 5 = 2x − 7 instantly. Type the equation or enter coefficients, and follow the worked steps to the value of x.

x = -12
Solution

Worked steps

  1. Left side collects to 3x + 5; right side to 2x − 7.
  2. Subtract 2x from both sides: 1x + 5 = -7
  3. Subtract 5 from both sides: 1x = -12
  4. Divide both sides by 1: x = -12 ÷ 1 = -12

Check: substituting x = -12 gives LHS = -31 and RHS = -31 — both sides match.

What is the Linear Equation Solver?

The ByteTools Linear Equation Solver finds x in any single-variable linear equation. Type the equation naturally — for example 3x + 5 = 2x − 7 or 4(missing terms are fine) — or switch to the structured ax + b = cx + d mode and fill in the four numbers.

  • Accepts typed equations like 5x - 3 = 2x + 9
  • Structured ax + b = cx + d input mode
  • Worked steps: collect x terms, move constants, divide
  • Detects no-solution and identity (all-x) cases
  • Verification by substituting x back into both sides
  • 100% private — runs entirely in your browser

How to use the Linear Equation Solver

  1. 1

    Type a linear equation such as 3x + 5 = 2x − 7, or switch to coefficient mode.

  2. 2

    In coefficient mode, fill in a, b, c and d for ax + b = cx + d.

  3. 3

    Read the value of x, or the no-solution / always-true verdict.

  4. 4

    Follow the worked steps showing how terms were collected.

  5. 5

    Copy the solution with one click.

About the Linear Equation Solver

The ByteTools Linear Equation Solver finds x in any single-variable linear equation. Type the equation naturally — for example 3x + 5 = 2x − 7 or 4(missing terms are fine) — or switch to the structured ax + b = cx + d mode and fill in the four numbers. A small built-in parser collects the x terms and constants on each side, so no special syntax is needed.

The solver prints each algebra step in plain language: collecting x terms on the left, moving constants to the right, and dividing by the final coefficient. It also handles the special cases honestly — equations with no solution (like x = x + 1) and identities that are true for every x (like 2x = 2x).

Everything runs 100% locally in your browser. Nothing is uploaded or stored, the answer updates as you type, and both the solution and the steps can be copied.

Frequently asked questions

How do you solve a linear equation step by step?

Collect all x terms on one side by subtracting the smaller x term from both sides, then move the plain numbers to the other side, and finally divide both sides by the coefficient of x. For 3x + 5 = 2x − 7 that gives x + 5 = −7, then x = −12.

What if the x terms cancel out completely?

Then the equation has no unique solution. If what remains is a true statement like 5 = 5, every value of x works — it is an identity. If it is false, like 0 = 3, no value of x works and the equation has no solution. The solver reports both cases explicitly.

What counts as a linear equation?

An equation where the variable appears only to the first power — no x², no square roots of x, no x in a denominator. Its graph is a straight line, and it has at most one solution. This tool handles one-variable linear equations; for x and y systems, use the system of equations solver.

Can I type decimals and negative numbers?

Yes. Equations like -2.5x + 1 = 0.5x - 11 parse fine, and the coefficient mode accepts any real numbers. The parser understands terms like x, -x, 3x and 4.2x on either side of the equals sign.

How does the solver check its answer?

It substitutes the computed x back into the left and right sides of your original equation and shows that both evaluate to the same number. That verification line is printed under the steps, so you can trust the result or spot a typo in the equation.

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