Linear equation inspector

Select the code and use your copy shortcut. Changes in this preview are temporary.

<!doctype html><html lang="en-US"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Linear equation inspector</title><style>*{box-sizing:border-box}:root{--ink:#24333d;--muted:#586872;--line:#cfd9de;--accent:#27627b;--soft:#edf3f5;--paper:white;color-scheme:light}body{margin:0;background:#f2f4f4;color:var(--ink);font:16px/1.5 system-ui,-apple-system,"Segoe UI",sans-serif}main{max-width:1100px;padding:28px 32px 64px;margin:auto}header{margin-bottom:20px}h1{font-size:clamp(1.5rem,3vw,2.1rem);letter-spacing:-.035em;line-height:1.18;margin:0 0 9px}h2{font-size:1.2rem;line-height:1.3;margin:0 0 15px}h3{font-size:1rem;margin:0 0 8px}p{margin:9px 0 16px}header p{margin-bottom:0}.eyebrow{font-size:.75rem;font-weight:750;text-transform:uppercase;letter-spacing:.12em;color:var(--accent);margin-bottom:8px}.muted,small{color:var(--muted)}.panel{background:var(--paper);border:1px solid var(--line);padding:24px;border-radius:12px}.grid{display:grid;grid-template-columns:minmax(0,1fr) minmax(0,1fr);gap:24px}.fields{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:15px}.triple{display:grid;grid-template-columns:2fr 1fr 1fr;gap:16px}.below{margin-top:24px}label{display:block;font-size:.9rem;font-weight:650}input,select,textarea,button{font:inherit}input,select,textarea{display:block;width:100%;min-width:0;margin-top:6px;padding:10px 12px;border:1px solid #879da8;border-radius:6px;background:white;color:var(--ink)}input,select{min-height:46px}textarea{resize:vertical;line-height:1.6}button{min-height:44px;border:1px solid var(--accent);border-radius:6px;padding:9px 15px;background:var(--accent);color:white;font-weight:650;cursor:pointer}button.secondary{background:white;color:var(--accent)}button:disabled{opacity:.5;cursor:not-allowed}button:hover:enabled{filter:brightness(.95)}:focus-visible{outline:3px solid #bb6b22;outline-offset:3px}.actions{display:flex;flex-wrap:wrap;gap:10px;margin-top:18px}.result{padding:26px;background:var(--ink);color:white;border-radius:12px}.result .muted{color:#d1e0e7}.big{font-size:clamp(2rem,5vw,3.5rem);line-height:1.15;letter-spacing:-.04em;font-weight:750;font-variant-numeric:tabular-nums;margin:10px 0;overflow-wrap:anywhere}.formula{font-family:ui-monospace,SFMono-Regular,Consolas,monospace;overflow-wrap:anywhere}.error{min-height:24px;color:#a33028;font-weight:650;margin:9px 0 0}.status{font-size:.9rem;color:var(--muted)}.note{padding:12px 16px;background:#fff3de;border-left:3px solid #b67e38;color:#65481d}table{width:100%;border-collapse:collapse;font-size:.92rem}th{text-align:left;color:var(--muted);font-size:.83rem}th,td{padding:10px 8px;border-bottom:1px solid var(--line);vertical-align:top}th:first-child,td:first-child{padding-left:0}details{padding:16px 0;border-top:1px solid var(--line)}summary{font-weight:650;cursor:pointer}pre{white-space:pre-wrap;overflow-wrap:anywhere;font:.87rem/1.6 ui-monospace,Consolas,monospace;background:#edf1f3;border:1px solid #d7e0e4;padding:18px;border-radius:7px}svg{display:block;width:100%;height:auto}.badge{display:inline-block;padding:3px 9px;background:var(--soft);color:var(--accent);font-size:.78rem;font-weight:700;border-radius:25px}.rule{height:1px;background:var(--line);margin:18px 0}[hidden]{display:none!important}a{color:var(--accent)}@media(max-width:720px){main{padding:22px 20px 45px}.grid{grid-template-columns:1fr;gap:18px}.panel{padding:20px}.triple{grid-template-columns:1fr 1fr}.triple>label:first-child{grid-column:1/-1}}@media(max-width:400px){main{padding:18px 16px 36px}.panel{padding:16px}.fields{gap:12px}.result{padding:20px}.big{font-size:2.2rem}th,td{padding:9px 5px}}:root{--accent:#78523d}body{background:#f3eee7}.equation-sheet{background:#fffdf8;border:1px solid #d9cbb8;border-top:5px solid #a78355;padding:28px}.equation{font:clamp(1.5rem,3vw,2rem)/1.3 ui-serif,Georgia,serif;border-bottom:1px solid #d9cbb8;padding-bottom:18px}.solve-line{display:grid;grid-template-columns:1fr 1fr;gap:20px;margin:20px 0}.solve-line .big{color:#765333}.substitute{align-self:center}.substitute b{display:block;font-size:1.8rem}.substitute .formula{font-size:.86rem;margin-top:8px}.coefficients{display:grid;grid-template-columns:repeat(4,minmax(0,1fr));gap:16px}@media(max-width:600px){.coefficients{grid-template-columns:1fr 1fr}.solve-line{grid-template-columns:1fr;gap:12px}.equation-sheet{padding:22px}.substitute{border-top:1px solid #d9cbb8;padding-top:12px}}</style></head><body><main><header><h1>Linear equation inspector</h1><p>Solve only ax + b = cx + d, with integer coefficients from −1000 to 1000.</p></header>
<section class="equation-sheet" aria-live="polite"><div id="equation" class="equation">4x + 3 = x + 15</div><div class="solve-line"><div><span id="classification" class="muted">One solution</span><div class="big" id="result">x = 4</div></div><div class="substitute"><span class="muted">Check in the original equation</span><b id="equality">19 = 19</b><div id="checkTrace" class="formula"></div></div></div><p id="reduction" class="formula">(4 − 1)x = 15 − 3 → 3x = 12</p></section>
<section class="panel below"><div class="coefficients"><label for="a">a · Left x coefficient<input id="a" value="4" inputmode="decimal" ></label><label for="b">b · Left constant<input id="b" value="3" inputmode="decimal" ></label><label for="c">c · Right x coefficient<input id="c" value="1" inputmode="decimal" ></label><label for="d">d · Right constant<input id="d" value="15" inputmode="decimal" ></label></div><div class="actions"><button type="button" id="solve">Solve</button><button type="button" id="reset" class="secondary">Reset 4x + 3 = x + 15</button></div><p id="error" role="status" class="error"></p><div class="below"><label for="case">Load another equation<select id="case"><option value="default">Choose a worked equation</option><option value="fraction">3x + 1 = x + 6</option><option value="none">2x + 5 = 2x + 8</option><option value="all">2x + 5 = 2x + 5</option></select></label></div></section>
<section class="below panel"><h2>Why this solution set?</h2><p id="reason"></p><p id="decimal" class="formula"></p></section><details class="below"><summary>Scope and method</summary><p>Subtract cx and b from both sides to obtain (a − c)x = d − b. Check the x coefficient before dividing. 0x = nonzero is a contradiction; 0x = 0 is an identity for every real x.</p><p>Exact integer fractions are reduced before substitution. A decimal is a display reference, not a replacement for that fraction. Blank, decimal, malformed, and out-of-range coefficients clear all results. No expressions, functions, quadratics, systems, learner assessment, or saved records.</p></details></main><script>const $=id=>document.getElementById(id),put=(id,s)=>{$(id).textContent=s};
function esc(s){return String(s).replace(/[&<>"']/g,c=>({'&':'&amp;','<':'&lt;','>':'&gt;','"':'&quot;',"'":'&#39;'}[c]));}
function gcd(a,b){a=a<0n?-a:a;b=b<0n?-b:b;while(b){[a,b]=[b,a%b]}return a||1n;}
function R(n,d=1n){n=BigInt(n);d=BigInt(d);if(d===0n)throw Error('Undefined denominator.');if(d<0n){n=-n;d=-d}const g=gcd(n,d);return {n:n/g,d:d/g};}
function mul(a,b){return R(a.n*b.n,a.d*b.d)}function div(a,b){return R(a.n*b.d,a.d*b.n)}function add(a,b){return R(a.n*b.d+b.n*a.d,a.d*b.d)}function sub(a,b){return R(a.n*b.d-b.n*a.d,a.d*b.d)}function cmp(a,b){const x=a.n*b.d-b.n*a.d;return x<0n?-1:x>0n?1:0}
function parse(s,{max=1000000,positive=false,places=6}={}){const t=String(s).trim();if(!t)throw Error('Enter a value; blank is not zero.');const re=new RegExp('^[0-9]+(?:\.[0-9]{1,'+places+'})?$');if(!re.test(t))throw Error('Use digits and a US decimal point, up to '+places+' places; no signs, commas, or exponents.');const v=Number(t);if(!Number.isFinite(v)||v>max||(positive&&v===0))throw Error('Value must be '+(positive?'greater than zero':'nonnegative')+' and at most '+max+'.');const [a,b='']=t.split('.');return R(BigInt(a+b),10n**BigInt(b.length));}
function format(a,places=6){const neg=a.n<0n,n=neg?-a.n:a.n,scale=10n**BigInt(places),v=n*scale,q=v/a.d,rem=v%a.d,k=q+(rem*2n>=a.d?1n:0n);const f=(k%scale).toString().padStart(places,'0').replace(/0+$/,'');return {text:(neg&&k!==0n?'-':'')+(k/scale)+(f?'.'+f:''),approx:rem!==0n};}
function exact(a){let d=a.d;while(d%2n===0n)d/=2n;while(d%5n===0n)d/=5n;if(d!==1n)return a.n+'/'+a.d;let places=0,p=1n;while(p%a.d!==0n&&places<40){p*=10n;places++}return format(a,places).text;}
function display(a,places=6){if(a.n>0n&&cmp(a,R(1n,10n**BigInt(places)))<0)return '< '+format(R(1n,10n**BigInt(places)),places).text;const f=format(a,places);return (f.approx?'≈ ':'')+f.text;}
function listen(ids,fn){ids.forEach(id=>{ $(id).addEventListener('input',fn);$(id).addEventListener('change',fn); });}

function integer(s,name){const t=String(s).trim();if(!/^-?\d+$/.test(t)||Number(t)<-1000||Number(t)>1000)throw Error(name+': enter an integer from -1000 to 1000; blank is not zero.');return BigInt(t);}
function expression(a,b){const x=a===1n?'x':a===-1n?'−x':a+'x';return x+(b<0n?' − '+(-b):' + '+b);}
function solve(a,b,c,d){const vals=[a,b,c,d].map((s,i)=>integer(s,['a','b','c','d'][i]));[a,b,c,d]=vals;const A=a-c,B=d-b;if(A===0n)return {vals,A,B,type:B===0n?'all':'none'};const x=R(B,A),left=add(mul(R(a),x),R(b)),right=add(mul(R(c),x),R(d));return {vals,A,B,type:'one',x,left,right};}
function fraction(a){return a.d===1n?String(a.n):a.n+'/'+a.d;}
function update(){try{const r=solve($('a').value,$('b').value,$('c').value,$('d').value),[a,b,c,d]=r.vals;put('equation',expression(a,b)+' = '+expression(c,d));put('reduction','('+a+' − ('+c+'))x = '+d+' − ('+b+') → '+r.A+'x = '+r.B);put('classification',r.type==='one'?'One solution':r.type==='all'?'Identity':'Contradiction');put('result',r.type==='one'?'x = '+fraction(r.x):r.type==='all'?'Every real x':'No solution');put('equality',r.type==='one'?fraction(r.left)+' = '+fraction(r.right):b+' '+(r.type==='all'?'=':'≠')+' '+d);put('checkTrace',r.type==='one'?a+' × ('+fraction(r.x)+') + ('+b+') = '+c+' × ('+fraction(r.x)+') + ('+d+')':'The x terms cancel before any division.');put('reason',r.type==='one'?'The reduced x coefficient is nonzero. Dividing gives a unique solution, which agrees on both original sides.':r.type==='all'?'Both sides reduce to the same expression. Every real x works; zero is only one of those values.':'Equal x coefficients cancel, leaving unequal constants. No value of x can make the equation true.');put('decimal',r.type==='one'?'Decimal reference: x '+(format(r.x,6).approx?'≈ ':'= ')+format(r.x,6).text:'No single-number solution or substitution is fabricated.');put('error','');}catch(e){put('result','—');['equation','reduction','classification','equality','checkTrace','reason','decimal'].forEach(id=>put(id,''));put('error',e.message);}}
listen(['a','b','c','d'],update);$('solve').addEventListener('click',update);function loadCase(values){['a','b','c','d'].forEach((id,i)=>$(id).value=values[i]);update()};$('reset').addEventListener('click',()=>{$('case').value='default';loadCase(['4','3','1','15'])});$('case').addEventListener('change',()=>loadCase(({default:['4','3','1','15'],fraction:['3','1','1','6'],none:['2','5','2','8'],all:['2','5','2','5']})[$('case').value]));globalThis.Tool={solve,update,exact,expression};update();</script></body></html>