⚖️ 一元一次方程：天平两边一样重⚖️ Linear Equations: the Balanced Scale
上一片里，机器人把多项式当成一列待加工的积木。可光会摆积木还不够——如果知道结果，能不能反推出未知的那块？能，这就是方程：一台必须保持平衡的天平。Last leaf, the robot treated polynomials as rows of number blocks to build with. But knowing the result, can we work backwards to the unknown block? Yes — with an equation: a scale that must stay balanced.
第 1 步：方程是一台天平Step 1: An equation is a scale
先看这台天平——它为什么必须水平？Start with this scale — why must it stay level?
等号“=”就是天平的横梁：左边 2x+3，右边 9，两边一样重。绿色袋子里装着同一个未知数 x，每个袋子一样重；金色砝码每个重 1。让天平平衡的那个 x，就叫方程的解——这里正等着你去找。The equals sign is the beam: 2x+3 on the left, 9 on the right, both weigh the same. Each green bag hides the same unknown x and weighs the same; each golden weight is 1. The x that keeps the scale level is the equation's solution — and it is waiting to be found.
那怎么把 x 单独“拎”出来，又不弄翻天平？So how do we isolate x without tipping the scale?
第 2 步：两边同做一件事Step 2: Do the same to both sides
规矩只有一条：两边同加、同减、同乘、同除。从两盘各拿走 3 个砝码，左边剩 2x，右边剩 6——天平照样水平。这就是“等价变形”：每一步都得到一台和原来同样平衡的新天平。One rule only: add, subtract, multiply or divide both sides the same way. Take 3 weights off each pan and the left leaves 2x, the right 6 — still level. This is an “equivalent transformation”: every step is a new scale that balances exactly like the old one.
2x 是两个 x 袋——怎么让它变成 1 个？2x means two identical x bags — how do we get down to one?
第 3 步：把 x 解出来Step 3: Solve for x
两边同除以 2：2x 变成 1 个 x，6 变成 3。读出来——x=3！一次方程的通关路线：去括号 → 移项（两边同加同减）→ 合并同类项 → 系数化为 1（两边同除）。因为未知数只有一个 x、次数只有 1，它就叫“一元一次方程”。Divide both sides by 2: 2x becomes one x bag and 6 becomes 3. Read it off — x=3! The standard route: clear brackets → move terms (add/subtract both sides) → combine like terms → divide by the coefficient. One unknown, degree one — that's a linear equation.
🎮 你来当平衡操作员（1 分钟）🎮 Your turn: balance operator (1 minute)
道理讲完了。拖走或加回砝码，永远两边同做一件事，把 4 个方程里的 x 解出来。Theory done. Take weights away or put them back — always doing the same to both sides — and solve for x in 4 equations.
一句话记住它：一元一次方程 = 一台天平；解方程 = 两边同做一件事，把 x 单独留下。Remember it in one line: a linear equation is a balance scale; solving it means doing the same thing to both sides until x stands alone.
方程是含未知数的等式，解就是让等号成立的那个数An equation is an equality with an unknown; the solution makes it true两边同加同减同乘同除（除数不为 0），天平永远平衡Add, subtract, multiply or divide both sides (never by 0) — the scale stays level一般步骤：移项 → 合并同类项 → 系数化为 1Standard steps: move terms → combine like terms → divide by the coefficient
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