超緊急! Inequality (40分) 有答案求步驟

1) x/6 + 9 > (2/3)x - 7
x/6 > 2/3x -16
x > 4x -96
96>3x
32>x
x<32

2) 2(9x+1) < 3(5x-1) - 4(3-x)
18x+2<15x-3 -12 +4x
17
x>17

3) (2x+3)/4 > 3/2 (2.5-x)
2x+3 > 6(2.5-x)
2x+3 > 15 -6x
8x>12
x > 12/8
x > 3/2

4) (5x-3)/3 ≦ (9x+3)/4
4(5x-3) ≦3(9x+3)
20x-12 ≦27x +9
-21 ≦ 7x
-3 ≦ x
x ≧ -3



2010-11-17 23:11:34 補充：
002

尾二的負數乘除需要轉方向....

好易錯... 所以人地問親, 我都盡量避免

002 is wrong
____________
(5x-3)/3 ≦ (9x+3)/4
4(5x-3) ≦ 3(9x+3)
20x-12 ≦ 27x+9
20x-27x ≦ 9+12
-7x ≦ 21-------------(the sign should be change)
x=>-3
________________
A way is for checking

Subsitute a number which is bigger than -3 such -2,-1,0...........

(1)
x/6 + 9 > (2/3)x - 7
(x+9*6)/6 > (2x-7*3)/3
x+54 > 2(2x-21)
x+54 > 4x-42
54+42 > 4x-x
96 > 3x
x < 96/3
x < 32

(2)
2(9x+1) < 3(5x-1) - 4(3-x)
18x+2 < 15x-3-12+4x
2+3+12 < 15x+4x-18x
17 < x
x > 17

(3)
(2x+3)/4 > 3/2 (2.5-x)
(2x+3)/4 > 3*2*(2.5-x) / 4
2x+3 > 15-6x
2x+6x > 15-3
8x > 12
2x > 3
x > (3/2)

(4)
(5x-3)/3 ≦ (9x+3)/4
4(5x-3) ≦ 3(9x+3)
20x-12 ≦ 27x+9
20x-27x ≦ 9+12
-7x ≦ 21
x ≦ [21/(-7)]
x ≦ -3 <== 同你ans唔同既!

2010-11-18 21:06:54 補充：
(4) 更正一下.....
(5x-3)/3 ≦ (9x+3)/4
4(5x-3) ≦ 3(9x+3)
20x-12 ≦ 27x+9
-12-9 ≦ 27x-20x
-21 ≦ 7x
7x ≧ -21
x ≧ -21/7
x ≧ -3

2010-11-18 21:08:27 補充：
(4) 更正一下.....
(5x-3)/3 ≦ (9x+3)/4
4(5x-3) ≦ 3(9x+3)
20x-12≦ 27x+9
-12-9 ≦ 27x-20x
-21 ≦ 7x
7x ≧ -21
x ≧ -21/7
x ≧ -3

2010-11-18 21:10:45 補充：
(4) 更正一下.....
(5x-3)/3 ≦ (9x+3)/4
4(5x-3) ≦ 3(9x+3)
20x-12 ≦ 27x+9
-12-9 ≦ 27x-20x
-21 ≦ 7x
7x ≧ -21
x ≧ -21/7
x ≧ -3

2010-11-18 21:13:01 補充：
(4) 更正一下.....
唔知點解變左火星文...
"<=" 等於 "細過及等於"
">=" 等於 "大過及等於"

(5x-3)/3 <= (9x+3)/4
4(5x-3) <= 3(9x+3)
20x-12 <= 27x+9
-12-9 <= 27x-20x
-21 <= 7x
7x >= -21
x >= -21/7
x >= -3