N Numeratibase

Free math tool

Linear Equation Solver

Solve one-variable linear equations in x, show the balancing steps, and catch no-solution and infinite-solution cases.

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2(x + 3) = 14 5x - 7 = 3x + 9 4x + 3 = 4x + 3

Direct answer

Infinitely many solutions

This equation is true for every x-value.

Solution set All real numbers

Steps

  1. Start with 4x+3=4x+3.
  2. Move everything to one side to get = 0.
  3. Both sides are identical, so every x-value works.

Why it works

A linear equation is balanced as long as you do the same operation to both sides. Combining like terms and isolating x makes the balance explicit.

Common mistakes

  • Distributing incorrectly before combining like terms.
  • Moving a term across the equals sign without changing its sign.
  • Treating identity or contradiction cases as if they had one numeric answer.

Worked examples

Solve 2(x + 3) = 14

Distribute to get 2x + 6 = 14, then subtract 6 and divide by 2 to get x = 4.

Solve 4x + 3 = 4x + 3

Both sides are identical, so every x-value works.

Practice

  • 3x + 5 = 20
  • 7 - 2x = 1
  • 6(x - 1) = 3x + 9