Linear equation solver
Enter 2x + 3 = 11 and get x equal to 4: subtract 3 from both sides, divide by 2, then check that 2 · 4 + 3 gives 11. When a is zero, you learn whether every number works or none does. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- A
- 2
- B
- 3
- C
- 11
- X
- 4
- Equation
- 2x + 3 = 11
- Isolated
- x = 4
- Solution type
- unique
A linear equation solver turns three numbers into the value of x that makes ax plus b equal c. Enter the coefficient of x, the constant term, and the right-hand side; the tool returns the isolated solution, a readable equation string, step-by-step isolation, and a substitution check. Homework checks, spreadsheet formulas, interview prep, and quick engineering rearrangements all need that same isolation without opening a computer-algebra system.
What ax + b = c means and how isolation works
A linear equation in one variable has the form a times x plus b equals c, where a, b, and c are known real numbers and x is the unknown. When a is not zero there is exactly one real solution: subtract b from both sides to get a times x equals c minus b, then divide both sides by a to isolate x equals open parenthesis c minus b close parenthesis divided by a.
That closed form is the entire solver; there is no iteration, no guessing, and no dependence on initial values. When a is zero the equation no longer involves x. Teachers and automated graders care about those two degenerate cases as much as the unique root: a student who divides by zero or claims x equals zero for a contradiction needs a different mark than a correct isolation.
The check step multiplies a by the computed x and adds b, then compares to c after the same rounding used for the published fields, so a successful unique solution always ships with a numeric check you can assert in tests or worksheets.
Practical tips, limits, and related searches
Keep coefficients and the right-hand side inside the published absolute range so division cannot produce a non-finite x that the solver must reject. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Near-zero coefficients with absolute value at or below one times ten to the minus fifteen are treated as zero so floating noise does not produce enormous roots that look like unique solutions.
When teaching, pair examples: two x plus three equals eleven yields x equals four; negative slope cases flip the isolation signs correctly; and zero times x plus five equals seven demonstrates the no-solution error path students must recognize on exams. This landing targets people searching for a linear equation solver, solve ax plus b equals c, or isolate x online; it is not a system of two equations, not a quadratic formula tool, and not a graphing calculator.
Prefer this capability when you already have the three coefficients; if your source is a word problem, extract a, b, and c first. Round-trip checks are easy: after a unique solution, recompute a times x plus b and confirm it equals c within the same rounding, and confirm that changing only c by one unit moves x by one over a when a is nonzero.
What you can do with it
Homework checks for one-step isolation
Students enter a, b, and c from textbook problems and compare hand-written x, equation string, and steps against a deterministic result before submitting.
Spreadsheet and form validation of linear rules
Backend scripts rearrange cost, rate, or threshold formulas written as ax + b = c and assert the isolated x matches business rules without a CAS dependency.
FAQ
How do you solve ax + b = c for x?
Subtract b from both sides, then divide by a (when a ≠ 0): x = (c − b) / a. This tool returns that value plus isolation steps and a substitution check.
What happens when a is zero?
If b equals c the equation is an identity (infinite solutions).
Does the solver handle fractions or decimals?
Yes. Send finite numbers (or strict numeric strings).
Can it solve systems or quadratics?
No. This capability only isolates x in a single linear equation ax + b = c. Use other tools for systems, polynomials, or inequalities.
Is the linear equation solver free?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/algebra/linear-equation \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"a":2,"b":3,"c":11}'const res = await fetch("https://api.kit.forhosting.com/algebra/linear-equation", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"a": 2,
"b": 3,
"c": 11
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/algebra/linear-equation",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"a": 2,
"b": 3,
"c": 11
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/algebra/linear-equation", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"a":2,"b":3,"c":11}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"a":2,"b":3,"c":11}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/algebra/linear-equation", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"a": 2,
"b": 3,
"c": 11
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "algebra.linear_equation",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
When the coefficient of x is zero and the constants disagree, the equation has no solution and the API returns a clear invalid_input error instead of a fake root.
What ax + b = c means and how isolation works
If b also equals c, every real number satisfies the statement—it is an identity—and this tool reports solution_type infinite with a null x and a clear message instead of inventing a single root. If a is zero and b differs from c, the left and right sides cannot match for any x, so the response is invalid_input with a no-solution message and no charge.
How to call the API and what comes back
Send a JSON body with three required finite numbers: a (aliases coeff_a and slope), b (aliases coeff_b and constant), and c (aliases rhs and right_hand_side). Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On a unique success the response echoes rounded a, b, and c, sets x to the isolated value, equation to a human-readable left equals right string, isolated to the string x equals the value, solution_type to unique, message to a short summary, steps to an ordered array of isolation and check lines, formula to the closed form x equals open parenthesis c minus b close parenthesis over a, and check to a times x plus b after rounding. On the identity path when a is zero and b equals c, x and isolated are null, solution_type is infinite, and steps explain that every real x works. Failed validation—missing fields, non-finite numbers, values outside absolute limits, or a equals zero with b not equal to c—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners type contradictions on purpose.
Integration use cases
Interview prep and coding kata expected values
Generate known-good unique roots and deliberate no-solution cases for unit tests of student code that claims to solve linear equations.