linear inequalities: x/2>1/4(1-x/3)?
回答 (6)
x/2>1/4(1-x/3)
12(x/2)>12*[1/4(1-x/3)]
6x>3(1-x/3)
6x>3-x
7x>3
x>3/7
(1/2)x > 1/4 [1-(1/3)x]
(1/2)x + (1/3)x > 1/4
6x + 4x > 3
10x > 3
x > 3/10
x/2>(1/4)(1-x/3)
2x>1-x/3
6x>3-x
4x>3
x>4/3
首先,要先知道 x≠3
因為如果x=3
那會造成1/4(1-x/3)無意義
x/2 > 1/4(1-x/3)
0 > 1/4(1-x/3) - x/2
[2x²-6x+3] / (3-x) < 0
由上得知
{x-[(3+√3) / 2]}*{x-[(3-√3) / 2]}*(3-x) < 0
答案 : x < (3-√3) / 2 or (3+√3) / 2 < x < 3 {x≠3也符合了}
收錄日期: 2021-04-18 00:19:49
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