maths!

解不等式︳2x－5︳+︳x－8︳>10。
Sol
2x－5=0 =>x=5/2
x－8=0 =>x=8
(1) x<=5/2------------(1)
2x<=5 =>2x－5<=0 =>|2x－5|=5－2x
x<=5/2 =>x－8<=5/2－8<0 =>|x－8|=8－x
︳2x－5︳+︳x－8︳>10
5－2x+8－x>10
13－3x>10
－3x>－3
x<1------------------(2)
綜合(1)(2) x<1------------(A)
(2) 5/2<=x<=8-----(3)
5<=2x =>2x－5>=0 =>|2x－5|=2x－5
x<=8 =>x－8<=0 =>|x－8|=8－x
︳2x－5︳+︳x－8︳>10
2x－5+8－x>10
x+3>10
x>7------------------(4)
綜合(3)(4) 7<x<=---------(B)
(3) 8<=x------------(5)
16<=2x =>2x－5>= 0 =>|2x－5|=2x－5
8<=x =>x－8>=0 =>|x－8|=x－8
︳2x－5︳+︳x－8︳>10
2x－5+x－8>10
3x－13>10
3x>23
x>23/3--------------(6)
綜合(5)(6) x>=8---------(C)
綜合(A)(B)(C) 1<x or 7<x

︳2x-5︳+︳x-8︳>10。
2x-5+x-8>10
3x-13>10
3x>10+13
x>23/3