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第 15 週 · 不等式與線性規劃 · 第 1 節

複合一元一次不等式(和 / 或 · 數線)

初中你會解一個不等式;高中要把兩個不等式用「和」或「或」連起來,並在數線上表示。用「重疊區」把交集、並集講透。

▶ 第一關: 解一次不等式 + 數線表示
x > 22 (open, not included)x ≥ 22 (solid, included)a solution is a whole range, not one number
< or >open = endpoint NOT taken≤ or ≥solid = endpoint taken
−2x > 6÷(−2)flip!x < −3multiply / divide by a NEGATIVE → flip the sign
▶ 第二關: 「和 (and)」= 交集(重疊區)
x > 2x < 6ANDoverlap: 2 < x < 6
3 < 2x − 1 ≤ 9+1 : 4 < 2x ≤ 10÷2 : 2 < x ≤ 5same op toall 3 parts
▶ 第三關: 「或 (or)」= 並集
x ≤ 2 OR x ≥ 525gap (2,5) is NOT a solutionunion = two separate pieces
AND (both) → narrow overlapOR (either) → wide union
⚔ BOSS: 三段式與複合不等式綜合
2 < x ≤ 52 open5 solidintegers: 3, 4, 5 (min 3, max 5)