求教一道数学题

cub103

65.If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10 ?



(1) On the number line, z is closer to 10 than it is to x.



(2) z = 5x

谢谢!

ALGT

0<x<10,

(1)
z is closer to 10 on the number line, means z is on the right to the middle point between x and 10, which is the arithmetic mean. so z>(10+x)/2

or: 10-z<z-x
so z>(10+x)/2

sufficient

(2)
z-(10+x)/2 = 5x-5-x/2=9/2x-5
0<x<10
so -5<9/2x-5<40

insufficient

cub103

非常感谢!
但想不通,怎么10-Z<Z-X. 我用代入法做的话,如果Z=9, X=8, 那不就是不成立了吗?