Type the whole equation
One box, total freedom — constants, decimals like 0.25, fractions like 1/2, parentheses, negatives, and the variable on one side or both. Any single letter works: x, y, n, t.
3(x - 4) = 2x + 1 ✓ parses
01
The instrument
One input, zero buttons. The instant your equation parses, the screen normalizes it, the verdict lands in big type, and the work beneath is the complete written proof — distribute, combine, collect, isolate, divide, check.
ONE VARIABLE · PARENTHESES · FRACTIONS · DECIMALS · NEGATIVES
TRY
EQ ①
x+
y=
EQ ②
x+
y=
FRACTIONS LIKE 1/2 · DECIMALS LIKE 0.25 · EMPTY COUNTS AS 0
TRY
THE WORK — FULL PROOFLIVE
EXACT RATIONAL CORE·
NO FLOATING POINT·
SOLVES AS YOU TYPE·
NOTHING LEAVES THE PAGE
02
How to use it
Six moves and you're fluent. The tool is designed to be read as much as used — every chip teaches, every step is copyable.
It solves as you type
No equals button. The instant your input becomes a well-formed equation, the screen normalizes it — real minus signs, tidy products like 3x — and the work area starts writing itself.
keystroke → parsed → solved
Follow the written proof
Every transformation appears on the record: distribute, combine like terms, collect the variables on one side, isolate, divide. Nothing happens that isn't shown on the page.
3x − 12 = 2x + 1 → x − 12 = 1
Read the answer every way
The big line is the friendliest form. Rows beneath give the exact fraction, the exact decimal — repeating blocks overlined, never rounded — and a substitution check into your original equation.
x = 13 · 27 = 27 ✓
Two unknowns? SYSTEM
Flip to the SYSTEM tab for a 2×2 — enter the six coefficients and watch elimination: align the x-coefficients, subtract, solve for y, back-substitute, check in the untouched equation.
① x + y = 6 ② x − y = 2 → (4, 2)
Learn from the chips
Every example chip is a miniature lesson — distribution, variables on both sides, fraction coefficients, an identity that collapses to 0 = 0, a system whose lines never meet.
tap a chip → watch the proof
case-file · worked exampleEXACT · NO ROUNDING
linear-equation-solver/
3(x − 4) = 2x + 1INPUT
3x − 12 = 2x + 1DISTRIBUTE
x − 12 = 1COLLECT
x = 13ISOLATE
÷ 1 — skippedDIVIDE
3(13 − 4) → 27 = 27CHECK ✓
x = 13SOLUTION
1 EQUATION SOLVED · 0 ROUNDING ERRORS
03
Frequently asked questions
The questions every algebra student asks about linear equations — answered with worked numbers.
Q1How do I solve a linear equation step by step?
Keep both sides balanced — whatever you do to one side, do to the other. Expand parentheses, combine like terms, move every variable term to one side, move the constants to the other, then divide by the variable's coefficient. For 3(x − 4) = 2x + 1: distribute to 3x − 12 = 2x + 1, subtract 2x to get x − 12 = 1, then add 12 to get x = 13. The solver writes exactly these lines.
Q2How do I solve an equation with parentheses?
Distribute first: multiply the factor outside the bracket into every term inside. 3(x − 4) = 2x + 1 becomes 3x − 12 = 2x + 1, and from there it is an ordinary two-sided equation. The solver displays the fully distributed line before it begins collecting terms.
Q3How do I solve equations with the variable on both sides?
Collect the variable terms. In 5x − 7 = 3x + 9, subtract 3x from both sides to get 2x − 7 = 9, add 7 to get 2x = 16, and divide by 2: x = 8. Try the 5x − 7 = 3x + 9 chip on the tool to see it worked.
Q4How do I solve a linear equation with fractions or decimals?
Treat them as exact numbers. x/2 + 1 = x/3 becomes ½x + 1 = ⅓x; collecting gives (½ − ⅓)x = −1, so ⅙x = −1 and x = −6. Decimals are converted to fractions the moment you type them — 0.5 is stored as 1/2 — so nothing is ever rounded mid-solution.
Q5What makes an equation linear?
A linear equation in one variable can be written ax + b = 0 with a ≠ 0: the variable has exponent 1, is never multiplied by itself, and never sits in a denominator. x² + 1 = 5 is quadratic; 6/x = 2 is not linear in x. This solver handles degree exactly 1 — and tells you plainly when something isn't.
Q6When does a linear equation have no solution — or infinitely many?
When the variable cancels out. 2x + 5 = 2x + 9 collapses to 5 = 9 — false for every x, so no solution. 2(x + 3) = 2x + 6 collapses to 0 = 0 — true for every x, an identity with infinitely many solutions. The solver announces which of the three verdicts (one solution, none, all reals) your equation earns.
Q7How do I solve a system of two linear equations?
By elimination: scale the equations until one variable's coefficients match, subtract to eliminate it, solve the remaining single-variable equation, then back-substitute. For ① x + y = 6 and ② x − y = 2, adding eliminates y: 2x = 8, so x = 4 and y = 2. The SYSTEM tab performs and displays each of these moves.
Q8Is it free, and does my equation leave the page?
Completely free — no sign-up, no locked steps. All parsing and arithmetic run locally in your browser; nothing is recorded or transmitted, and once the page has loaded it keeps working offline.