Two-sided linear equation solver

Variables on Both Sides Calculator

Enter an equation with x on both sides and see how variable terms are collected before x is isolated.

Try an example

Why x can appear on both sides

Equations such as 5x - 3 = 2x + 12 are still linear. Solving starts by moving variable terms to one side and constants to the other while keeping the equation balanced.

When the x terms cancel completely, the remaining statement determines whether there is no solution or infinitely many solutions.

How the calculator collects terms

The solver subtracts or adds the variable term from one side, then moves the remaining constant and divides by the final x coefficient when necessary.

For identities and contradictions, the calculator stops at the logical result instead of attempting an invalid division by zero.

Try an example

Type or paste an equation, solve it, inspect the transformations, and use verification and the graph instead of relying on the final value alone.

5x - 3 = 2x + 12
7x + 4 = 3x + 20
2(x + 3) = x + 10
2x + 5 = 2x + 9

Worked examples

Follow the same steps the calculator uses for three equations in this category.

5x - 3 = 2x + 12

x = 5

  1. Subtract 2x from both sides

    5x-3=2x+123x-3=12

  2. Add 3 to both sides

    3x-3=123x=15

  3. Divide both sides by 3

    3x=15x=5

Verified

7x + 4 = 3x + 20

x = 4

  1. Subtract 3x from both sides

    7x+4=3x+204x+4=20

  2. Subtract 4 from both sides

    4x+4=204x=16

  3. Divide both sides by 4

    4x=16x=4

Verified

2(x + 3) = x + 10

x = 4

  1. Subtract x from both sides

    2x+6=x+10x+6=10

  2. Subtract 6 from both sides

    x+6=10x=4

Verified

Common mistakes

  • Enter a complete equation with an equals sign.
  • This equation type is not supported yet.
  • Substitute each answer into the original equation and compare both sides.

Frequently asked questions

What does this calculator support?
Collect x terms from equations such as 5x - 3 = 2x + 12.
How does it verify an answer?
Substitute each answer into the original equation and compare both sides.
Which equations are outside the supported range?
Cubic and higher-degree polynomials, logarithmic, exponential, trigonometric, nested-radical, and multiple-absolute-value equations remain outside the supported solver scope.

Verification

Substitute each answer into the original equation and compare both sides.

Current solver scope

Cubic and higher-degree polynomials, logarithmic, exponential, trigonometric, nested-radical, and multiple-absolute-value equations remain outside the supported solver scope.