HesapHanem

Linear Equation Solver

Enter the coefficients of your equation ax + b = c to solve for x instantly.

How it is calculated

The tool solves a·x + b = c by isolating x: subtract b from both sides, then divide by a, so x = (c − b) / a. You enter the three numbers a, b and c exactly as they appear in the equation, with their signs. The result is rounded to four decimals, so a repeating value such as one third is shown as 0.3333; only that rounded value is displayed, not the intermediate steps. If a is zero, the equation has no single solution (either none or infinitely many), so the tool returns no result. Negative and decimal coefficients are accepted. To handle an equation with x on both sides, first collect the x terms into one coefficient a.

Worked example

Solve 4x + 5 = 22, so a = 4, b = 5, c = 22. Step 1: subtract b from both sides, 22 − 5 = 17. Step 2: divide by a, 17 / 4 = 4.25. The tool prints 4.2500. Check: 4 × 4.25 + 5 = 17 + 5 = 22, as required.

Try this example →

Common mistakes

  • Entering b with the wrong sign. For 4x − 5 = 22 you must type b = −5, which gives x = 6.75, not 4.25.
  • Dividing by a before subtracting b, which gives (c / a) − b. The offset b has to be removed first.
  • Entering an equation like 3x + 2 = x + 10 directly. Move the x terms first: 2x + 2 = 10, so a = 2, b = 2, c = 10.
  • Entering a = 0 when the unknown cancels out. Such an equation has no single answer and the tool returns nothing.

About this calculator

An equation of the form ax + b = c is the standard first-degree (linear) equation taught at the start of algebra: a single unknown, x, appears only to the first power, multiplied by a coefficient a and offset by a constant b, set equal to another constant c. Solving it is a two-step isolation process — subtract b from both sides, then divide by a — and it's the algebraic building block that every more complex equation (quadratics, systems of equations, word problems) eventually reduces to at some step.

Students use a linear equation solver to check the final answer of their homework against their own working (the calculator shows the result, not the individual steps), while the same ax + b = c structure shows up constantly outside the classroom wherever a quantity scales proportionally with an offset — converting units, splitting a fixed cost across a variable number of items, or working out a break-even point in a simple pricing model.

This calculator takes the coefficients a, b, and c and returns the value of x rounded to four decimal places. The coefficient a cannot be zero.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators