505 lines
20 KiB
TypeScript
505 lines
20 KiB
TypeScript
import React, { useRef, useState, useEffect } from "react";
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import {
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ArrowDown,
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Check,
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BookOpen,
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Scale,
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ArrowRight,
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RotateCcw,
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} from "lucide-react";
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import LinearSolutionsWidget from "../../../components/lessons/LinearSolutionsWidget";
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import Quiz from "../../../components/lessons/Quiz";
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import { LINEAR_EQ_QUIZ_DATA } from "../../../utils/constants";
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import { Frac } from "../../../components/Math";
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interface LessonProps {
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onFinish?: () => void;
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}
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const BalanceScaleWidget = () => {
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const [left, setLeft] = useState(15);
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const [right, setRight] = useState(15);
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const [tilt, setTilt] = useState(0);
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const [message, setMessage] = useState("Balanced");
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const apply = (val: number, side: "both" | "left" | "right") => {
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let newLeft = left;
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let newRight = right;
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if (side === "left" || side === "both") newLeft += val;
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if (side === "right" || side === "both") newRight += val;
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setLeft(newLeft);
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setRight(newRight);
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if (newLeft === newRight) {
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setTilt(0);
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setMessage("Perfectly Balanced! ✅");
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} else if (newLeft > newRight) {
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setTilt(-15);
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setMessage("Unbalanced! Left side is heavier. ❌");
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} else {
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setTilt(15);
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setMessage("Unbalanced! Right side is heavier. ❌");
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}
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};
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const reset = () => {
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setLeft(15);
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setRight(15);
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setTilt(0);
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setMessage("Balanced");
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};
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return (
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<div className="bg-white p-6 rounded-xl shadow-lg border border-slate-200">
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<div className="flex justify-between items-center mb-8">
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<h3 className="font-bold text-slate-700">Algebra Balance Scale</h3>
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<button onClick={reset} className="text-slate-400 hover:text-slate-600">
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<RotateCcw className="w-4 h-4" />
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</button>
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</div>
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<div className="relative h-40 w-full mb-8 flex justify-center items-end">
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<div className="absolute bottom-0 w-0 h-0 border-l-[20px] border-l-transparent border-r-[20px] border-r-transparent border-b-[40px] border-b-slate-800"></div>
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<div
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className="w-64 h-2 bg-slate-600 absolute bottom-[40px] transition-transform duration-700"
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style={{ transform: `rotate(${tilt}deg)` }}
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>
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<div
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className="absolute left-0 top-0 flex flex-col items-center"
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style={{ transform: `translateY(0px) rotate(${-tilt}deg)` }}
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>
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<div className="w-20 h-20 border-b-4 border-l-2 border-r-2 border-slate-400 rounded-b-xl bg-slate-50 flex items-center justify-center shadow-inner relative top-2">
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<span className="font-bold text-blue-600 text-lg">{left} kg</span>
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</div>
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<div className="w-0.5 h-16 bg-slate-400 absolute -top-16"></div>
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</div>
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<div
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className="absolute right-0 top-0 flex flex-col items-center"
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style={{ transform: `translateY(0px) rotate(${-tilt}deg)` }}
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>
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<div className="w-20 h-20 border-b-4 border-l-2 border-r-2 border-slate-400 rounded-b-xl bg-slate-50 flex items-center justify-center shadow-inner relative top-2">
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<span className="font-bold text-emerald-600 text-lg">
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{right} kg
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</span>
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</div>
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<div className="w-0.5 h-16 bg-slate-400 absolute -top-16"></div>
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</div>
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</div>
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</div>
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<div
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className={`text-center font-bold mb-6 ${tilt === 0 ? "text-green-600" : "text-rose-600"}`}
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>
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{message}
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</div>
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<div className="grid grid-cols-2 gap-4">
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<button
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onClick={() => apply(-5, "left")}
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className="p-3 rounded-lg border-2 border-slate-200 hover:border-rose-300 hover:bg-rose-50 text-slate-600 text-sm font-bold transition-all"
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>
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Subtract 5 from Left ONLY
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</button>
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<button
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onClick={() => apply(-5, "both")}
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className="p-3 rounded-lg border-2 border-blue-500 bg-blue-50 hover:bg-blue-100 text-blue-700 text-sm font-bold transition-all shadow-sm"
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>
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Subtract 5 from BOTH sides
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</button>
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</div>
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<p className="text-xs text-center text-slate-400 mt-4">
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Goal: Keep the scale balanced while isolating the variable.
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</p>
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</div>
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);
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};
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const LinearEquationsLesson: React.FC<LessonProps> = ({ onFinish }) => {
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const [activeSection, setActiveSection] = useState(0);
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const sectionsRef = useRef<(HTMLElement | null)[]>([]);
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const scrollToSection = (index: number) => {
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setActiveSection(index);
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sectionsRef.current[index]?.scrollIntoView({
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behavior: "smooth",
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block: "start",
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});
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};
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useEffect(() => {
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const observer = new IntersectionObserver(
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(entries) => {
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entries.forEach((entry) => {
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if (entry.isIntersecting) {
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const index = sectionsRef.current.indexOf(
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entry.target as HTMLElement,
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);
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if (index !== -1) setActiveSection(index);
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}
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});
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},
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{ rootMargin: "-20% 0px -60% 0px" },
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);
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sectionsRef.current.forEach((section) => {
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if (section) observer.observe(section);
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});
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return () => observer.disconnect();
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}, []);
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const SectionMarker = ({
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index,
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title,
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icon: Icon,
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}: {
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index: number;
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title: string;
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icon: any;
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}) => {
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const isActive = activeSection === index;
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const isPast = activeSection > index;
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return (
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<button
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onClick={() => scrollToSection(index)}
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className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-blue-100" : "hover:bg-slate-100"}`}
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>
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<div
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className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-blue-600 text-white" : isPast ? "bg-blue-400 text-white" : "bg-slate-200 text-slate-500"}`}
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>
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{isPast ? (
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<Check className="w-4 h-4" />
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) : (
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<Icon className="w-4 h-4" />
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)}
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</div>
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<div className="text-left">
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<p
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className={`text-sm font-bold ${isActive ? "text-blue-900" : "text-slate-600"}`}
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>
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{title}
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</p>
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</div>
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</button>
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);
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};
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return (
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<div className="flex flex-col lg:flex-row min-h-screen">
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<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 z-0 hidden lg:block">
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<nav className="space-y-2">
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<SectionMarker index={0} title="The Balance Principle" icon={Scale} />
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<SectionMarker
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index={1}
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title="Number of Solutions"
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icon={ArrowRight}
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/>
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<SectionMarker index={2} title="Practice" icon={BookOpen} />
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</nav>
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</aside>
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<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
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{/* Section 1: Balance Principle */}
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<section
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ref={(el) => {
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sectionsRef.current[0] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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The Balance Principle
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-6">
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<p>
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Linear equations are like a balance scale. Whatever you do to one
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side, you <strong>must</strong> do to the other. The goal is
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always to <strong>isolate the variable</strong> — get x by itself
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on one side with a number on the other.
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</p>
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</div>
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<BalanceScaleWidget />
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{/* 4-Step Process */}
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<div className="mt-8 bg-blue-50 border border-blue-200 rounded-2xl p-6 space-y-4">
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<h3 className="font-bold text-blue-900 text-lg">
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The 4-Step Solve Process
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</h3>
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<div className="space-y-3">
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{[
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{
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step: "1",
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title: "Distribute",
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desc: "Expand parentheses and clear fractions by multiplying through by the LCD (lowest common denominator).",
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},
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{
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step: "2",
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title: "Combine Like Terms",
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desc: "Simplify each side of the equation separately — add/subtract terms with the same variable.",
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},
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{
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step: "3",
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title: "Move",
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desc: "Get all variable terms on one side, all constant terms on the other, using addition or subtraction.",
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},
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{
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step: "4",
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title: "Divide",
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desc: "Divide both sides by the coefficient of the variable to solve.",
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},
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].map((item) => (
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<div
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key={item.step}
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className="flex gap-4 bg-white rounded-xl p-4 border border-blue-100"
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>
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<div className="w-8 h-8 bg-blue-600 text-white rounded-full flex items-center justify-center font-bold shrink-0">
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{item.step}
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</div>
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<div>
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<p className="font-bold text-slate-800">{item.title}</p>
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<p className="text-slate-600 text-sm">{item.desc}</p>
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</div>
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</div>
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))}
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</div>
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</div>
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{/* Three Worked Examples */}
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<div className="mt-8 space-y-4">
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<div className="bg-emerald-50 border border-emerald-200 rounded-xl p-6">
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<p className="font-bold text-emerald-800 mb-3">
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Example 1: Basic (no fractions)
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</p>
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<div className="font-mono text-sm space-y-1 text-slate-700">
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<p>Solve: 3(2x − 4) = 2x + 8</p>
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<p className="text-slate-500">
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Step 1 (Distribute): 6x − 12 = 2x + 8
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</p>
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<p className="text-slate-500">Step 3 (Move): 4x = 20</p>
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<p className="text-slate-500">
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Step 4 (Divide by 4):{" "}
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<strong className="text-emerald-700">x = 5</strong>
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</p>
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</div>
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</div>
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<div className="bg-emerald-50 border border-emerald-200 rounded-xl p-6">
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<p className="font-bold text-emerald-800 mb-3">
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Example 2: With fractions — clear them first!
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</p>
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<div className="font-mono text-sm space-y-1 text-slate-700">
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<p>
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Solve: <Frac n="x" d="3" /> + 2 = <Frac n="x" d="2" /> − 1
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</p>
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<p className="text-slate-500">
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Multiply every term by 6 (LCD of 3 and 2):
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</p>
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<p className="text-slate-500">2x + 12 = 3x − 6</p>
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<p className="text-slate-500">12 + 6 = 3x − 2x</p>
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<p className="text-slate-500">
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<strong className="text-emerald-700">x = 18</strong>
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</p>
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</div>
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</div>
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<div className="bg-emerald-50 border border-emerald-200 rounded-xl p-6">
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<p className="font-bold text-emerald-800 mb-3">
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Example 3: Literal equations (isolating a variable)
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</p>
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<div className="font-mono text-sm space-y-1 text-slate-700">
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<p>Solve for r: A = P(1 + rt)</p>
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<p className="text-slate-500">
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Divide both sides by P: <Frac n="A" d="P" /> = 1 + rt
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</p>
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<p className="text-slate-500">
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Subtract 1: <Frac n="A" d="P" /> − 1 = rt
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</p>
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<p className="text-slate-500">
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Divide by t:{" "}
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<strong className="text-emerald-700">
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r ={" "}
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<Frac
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n={
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<>
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<Frac n="A" d="P" /> − 1
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</>
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}
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d="t"
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/>
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</strong>
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</p>
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</div>
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</div>
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</div>
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<div className="mt-6 bg-red-50 border border-red-200 rounded-xl p-4 text-sm">
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<p className="font-bold text-red-800 mb-1">
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Common SAT Mistake: Distributing a Negative
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</p>
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<p className="text-slate-700">
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When distributing a negative sign: −3(x − 4) = −3x + 12, NOT −3x −
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12. The negative multiplies EVERY term inside the parentheses.
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</p>
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</div>
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<button
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onClick={() => scrollToSection(1)}
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className="mt-8 group flex items-center text-blue-600 font-bold hover:text-blue-800 transition-colors"
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>
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Next: Number of Solutions{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 2: Number of Solutions */}
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<section
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ref={(el) => {
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sectionsRef.current[1] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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One, None, or Infinite Solutions?
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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Not all equations have exactly one answer. After simplifying, look
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at what's left. The SAT frequently asks for a value of <em>k</em>{" "}
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that makes an equation have no solution or infinitely many
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solutions — this is a critical concept to master.
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</p>
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</div>
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<div className="bg-blue-50 border border-blue-200 rounded-2xl p-6 mb-8 space-y-4">
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<h3 className="text-lg font-bold text-blue-900">
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The Three Outcomes
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</h3>
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<div className="grid grid-cols-1 md:grid-cols-3 gap-4">
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<div className="bg-blue-100 rounded-xl p-4 text-center">
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<div className="font-bold text-blue-900 text-base mb-2">
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One Solution
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</div>
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<div className="font-mono text-sm text-blue-700 bg-white rounded p-2 mb-2">
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2x + 1 = x + 5
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</div>
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<div className="text-xs text-blue-700">
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Variable survives after simplification → unique answer:{" "}
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<strong>x = 4</strong>
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</div>
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</div>
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<div className="bg-red-50 border border-red-200 rounded-xl p-4 text-center">
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<div className="font-bold text-red-900 text-base mb-2">
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No Solution
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</div>
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<div className="font-mono text-sm text-red-700 bg-white rounded p-2 mb-2">
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2x + 3 = 2x + 5
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</div>
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<div className="text-xs text-red-700">
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Variables cancel → <strong>3 = 5</strong> (false statement —
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impossible)
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</div>
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</div>
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<div className="bg-emerald-50 border border-emerald-200 rounded-xl p-4 text-center">
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<div className="font-bold text-emerald-900 text-base mb-2">
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Infinite Solutions
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</div>
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<div className="font-mono text-sm text-emerald-700 bg-white rounded p-2 mb-2">
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2x + 3 = 2x + 3
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</div>
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<div className="text-xs text-emerald-700">
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Variables cancel → <strong>3 = 3</strong> (always true — every
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x works)
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</div>
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</div>
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</div>
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</div>
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{/* Finding k */}
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<div className="bg-blue-50 border border-blue-200 rounded-2xl p-6 mb-8 space-y-4">
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<h3 className="text-lg font-bold text-blue-900">
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SAT Focus: Finding the Value of k
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</h3>
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<div className="bg-white rounded-xl p-5 border border-blue-100">
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<p className="font-bold text-blue-800 mb-3">
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Example: For what value of k does 4x + k = 4x − 2 have no
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solution?
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</p>
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<div className="font-mono text-sm text-slate-700 space-y-1">
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<p>After subtracting 4x from both sides: k = −2</p>
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<p>
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If k = −2: −2 = −2 (always true) → infinite solutions, not no
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solution!
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</p>
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<p className="text-blue-700 font-bold">
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For no solution: k ≠ −2 (any other value gives a false
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statement like k = −2 being false)
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</p>
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</div>
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<p className="text-slate-500 text-xs mt-2">
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The equation has no solution for any value of k EXCEPT −2. For
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infinite solutions, set k = −2.
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</p>
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</div>
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<div className="bg-white rounded-xl p-5 border border-blue-100">
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<p className="font-bold text-blue-800 mb-3">
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Example: For what value of k does 3(x + k) = 3x + 12 have
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infinite solutions?
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</p>
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<div className="font-mono text-sm text-slate-700 space-y-1">
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<p>Distribute: 3x + 3k = 3x + 12</p>
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<p>Subtract 3x: 3k = 12</p>
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<p className="text-blue-700 font-bold">k = 4</p>
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</div>
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<p className="text-slate-500 text-xs mt-2">
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For k = 4: 12 = 12 (always true) → infinite solutions. ✓
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</p>
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</div>
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<div className="bg-red-50 border border-red-200 rounded-xl p-4 text-sm">
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<p className="font-bold text-red-800 mb-1">The Key Rule</p>
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<p className="text-slate-700">
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<strong>No solution</strong>: same variable coefficients,
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different constants (parallel lines).
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<br />
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<strong>Infinite solutions</strong>: same variable coefficients
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AND same constants (identical lines).
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</p>
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</div>
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</div>
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||
<LinearSolutionsWidget />
|
||
<button
|
||
onClick={() => scrollToSection(2)}
|
||
className="mt-12 group flex items-center text-blue-600 font-bold hover:text-blue-800 transition-colors"
|
||
>
|
||
Next: Practice Quiz{" "}
|
||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||
</button>
|
||
</section>
|
||
|
||
{/* Section 3: Quiz */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[2] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
|
||
Practice Time
|
||
</h2>
|
||
{LINEAR_EQ_QUIZ_DATA.map((quiz, idx) => (
|
||
<div key={quiz.id} className="mb-12">
|
||
<Quiz data={quiz} />
|
||
</div>
|
||
))}
|
||
<div className="p-8 bg-blue-900 rounded-2xl text-white text-center mt-12">
|
||
<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
|
||
<button
|
||
onClick={onFinish}
|
||
className="px-6 py-3 bg-white text-blue-900 font-bold rounded-full hover:bg-blue-50 transition-colors"
|
||
>
|
||
Finish Lesson ✓
|
||
</button>
|
||
</div>
|
||
</section>
|
||
</div>
|
||
</div>
|
||
);
|
||
};
|
||
|
||
export default LinearEquationsLesson;
|