Linear Equation Solver – ax + b = 0 Steps

A linear equation in one variable isolates x in a single move: subtract b, then divide by a. Take 3x + 12 = 0. Subtract 12 from both sides to get 3x = -12, then divide by 3, giving x = -4. Verification by substitution returns 3(-4) + 12 = -12 + 12 = 0, confirming the root. The solver handles fractional coefficients such as (2/3)x - 4 = 0, where multiplying both sides by 3/2 yields x = 6, and decimals like 0.5x = 7 with x = 14. Edge cases are flagged explicitly: if a = 0 and b ≠ 0 the equation has no solution (0x = -b is impossible), while a = 0 and b = 0 is an identity true for every x. Each transformation is printed so the method mirrors standard algebra classwork.

1. 1

   Enter a and b

   Type the coefficients of ax + b = 0

2. 2

   Isolate the x term

   Subtract b from both sides: ax = -b

3. 3

   Divide by a

   Compute x = -b/a, exact or decimal as needed

4. 4

   Verify the solution

   Substitute x back; the left side must equal 0

• 1

  One linear equation in one unknown always has exactly one root when a ≠ 0

• 2

  Fractional coefficients clear instantly when you multiply by the LCD

• 3

  Substitution is the fastest error check for any solved x

• Dividing only the bx side by a and leaving b undivided

• Sign slip moving b across the equals sign: 3x = -12, not +12

• Missing the a = 0 special cases — no solution or infinitely many

• Rounding decimals too early and losing exact checks