🚧 不等式：限高杆下的世界🚧 Inequalities: the world under the height bar
上一片，机器人靠着交点找到了交货点，那里只有一个 (x, y)。可今天送货路上立着一根限高杆：能过去的不是“一个高度”，而是所有低于 4 米的高度。不等式的答案，是一整段。Last leaf, the robot found the delivery point — a single (x, y). But today a height bar stands over the road: what fits is not one height but every height under 4 m. An inequality answers with a whole stretch.
第 1 步：答案是一片，不是一个点Step 1: A whole stretch, not a dot
限高杆到底在说什么？What is the height bar actually saying?
限高 4 米，意思是 h < 4：只要车高 h 比 4 小，就能过去。3.9 能过，2 能过，就连 3.99 也能过——3.9 和 4 之间还有无数个数。所以不等式的解是一整段，画出来是一条线段，而不是一个点。“Height limit 4 m” means h < 4: as long as the truck's height h is under 4, it fits. 3.9 fits, 2 fits, even 3.99 fits — between any two values there is always another. So an inequality's answer is a whole stretch: a segment, not a dot.
一片数不清的高度，怎么一眼说清？How can one picture describe countless heights at once?
第 2 步：把“一片”画在数轴上Step 2: Draw the stretch on a number line
数轴是最好的画布：h < 4 涂满 4 左边的所有位置，在 4 上画空心圆（表示不含 4）；如果是 h ≤ 4，空心圆变实心——4 也算数。解不等式像解方程一样移项：h + 1 < 4.5，两边同减 1，得 h < 3.5，整段区间跟着一起平移。A number line is the best canvas: h < 4 colours everything left of 4 and marks 4 with a hollow circle (4 itself is excluded); for h ≤ 4 the circle turns solid — 4 counts too. Solving works like equations: h + 1 < 4.5, subtract 1 from both sides, h < 3.5, and the whole stretch slides along.
移项这么好用，那有没有会让整片解“翻面”的操作？Shifting works well — but is there an operation that flips the whole stretch?
第 3 步：两边乘负数，方向要翻Step 3: Multiply by a negative — flip the sign
天平微微倾斜：8 > 5 成立。两边同时乘 −1 呢？得到 −8 < −5——秤盘像照镜子翻了个面，大于号也翻成小于号！这是不等式唯一要小心的规则：两边同乘（或同除）一个负数，不等号必须掉头。A balance tilts slightly: 8 > 5. Now multiply both sides by −1: −8 < −5 — the pans mirror-flip, and “>” flips into “<”! That is the one rule to watch: multiply or divide both sides by a negative number, and the inequality sign must turn around.
🎮 你来当司机（30 秒）🎮 Your turn: take the wheel (30 seconds)
拖动滑块调车高，数轴上的绿色段实时亮起——让 h 落进绿色段，再按“试着开过去”。Drag the slider to set the truck's height; the green stretch on the number line updates live. Land inside it, then press “Try to drive through”.
一句话记住它：方程的解是一个点，不等式的解是一整段区间；画在数轴上——< 空心、≤ 实心，两边乘负数要变号。Remember it in one line: an equation answers with a point, an inequality with a whole stretch; on a number line “<” is hollow and “≤” is solid — and multiplying by a negative flips the sign.
不等式的解是一整段：h < 4 表示所有比 4 小的数The answer is a stretch: h < 4 means every number smaller than 4数轴上：< 用空心圆（不含端点），≤ 用实心圆（含端点）On the number line: “<” hollow (endpoint excluded), “≤” solid (endpoint included)两边同乘或同除负数，不等号必须变方向Multiply or divide both sides by a negative — the sign must flip
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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