数学：定义新运算符号“*”的运算过程为a*b=[(1/2)a]-[(1/3)b],试解方程2*(2*x)=1*x.【“/

根据定义: 2*(2*x) = 2*[(1/2)×2 -(1/3)x]
= 2*[ 1 - (1/3)x]
= (1/2)×2 - (1/3)[1 - (1/3)x]
= 1 - 1/3 + (1/9)x = 2/3 + (1/9)x
1*x = (1/2)×1 -(1/3)x = 1/2 - (1/3)x
由于 2*(2*x) = 1*x
所以有: 2/3 + (1/9)x = 1/2 - (1/3)x
(1/9)x + (1/3)x = 1/2 - 2/3
(1/9 + 1/3)x = - 1/6
(4/9)x = - 1/6
x = -(1/6)/(4/9)
x = -3/8