Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Solve ax + b = c for x instantly.
4.0000
A linear equation in one variable has the form ax + b = c. This tool isolates x and gives the exact solution instantly.
Enter the coefficients a, b, and c for the equation ax + b = c. The value of x appears instantly (a cannot be 0).
x = (c - b) / a
Derived by subtracting b from both sides, then dividing both sides by a.
The page shows one case with a positive coefficient. Consider 3x - 7 = 5. Here a = 3, b = -7, c = 5. The tool computes x = (5 - (-7)) / 3 = 12 / 3 = 4. Now a negative coefficient: -2x + 1 = 9 means a = -2, b = 1, c = 9, so x = (9 - 1) / -2 = -4. A decimal case: 0.5x + 2 = 2.75 gives x = 0.75 / 0.5 = 1.5. The answer is displayed to four decimal places, so a result like one third appears as 0.3333.
x = (c - b) / a. Example: 4x - 6 = 10 has a = 4, b = -6, c = 10, so x = (10 + 6) / 4 = 4
Many word problems fit the pattern once you identify the pieces. If a taxi charges a flat fee of 3 plus 2 per kilometer and your fare was 17, the equation is 2x + 3 = 17, so a = 2, b = 3, c = 17, and x = 7 kilometers. If you have 40 saved and add 5 each week until you reach 100, then 5x + 40 = 100 gives x = 12 weeks. If a subscription costs a fixed setup fee plus a monthly charge, the same structure applies.
Always substitute the answer back into the original equation. For x = 4 in 3x - 7 = 5, you get 12 - 7 = 5, which is correct. This catches sign errors, the most common mistake when typing b. If b is subtracted in your equation, enter it as a negative number.
If you enter 0 for a, the equation has no x term and the tool cannot find a single value for x. In that situation, either every number satisfies the equation (when b equals c, such as 0x + 5 = 5) or none does (such as 0x + 5 = 8). The tool does not distinguish between the two, so work out which applies by comparing b and c yourself. Equations with an x² term, or with x in a denominator or under a root, are outside its scope and need to be simplified or solved with a different method, such as the Quadratic Equation Solver.
Because results are rounded to four decimals, a recurring decimal is an approximation. For an exact answer, work with the fraction (c - b) / a.
The equation isn't solvable for a unique x -- either every value of x works (if b also equals c) or no value does.
Rearrange it first by moving all x-terms to one side and constants to the other, then it fits the ax + b = c form.
No -- for equations with an x² term, use the Quadratic Equation Solver.
Treat the subtraction as adding a negative. Enter a = 2, b = -5, and c = 9, which gives x = (9 + 5) / 2 = 7.
Yes. The tool handles negative and non-integer answers, showing them to four decimal places.
No, it solves a single-variable equation. Systems with two unknowns need a different method.
Dividing by zero is undefined, and with no x term there is no single solution to display. Check whether b equals c to see if every value works or none does.
Reference: NIST Weights and Measures