Question

试用简便方法解方程1/2(X-1/2(X-1)+1)=2/3(X-1)

试用简便方法解方程1/2(X-1/2(X-1)+1)=2/3(X-1)

Answer 1

1/2(x-1/2(x-1)-1+2)=2/3(x-1) {将“+1”变为“-1+2”}
1/2((x-1)-1/2(x-1)+2)=2/3(x-1) → 1/2(1/2(x-1)+2)=2/3(x-1)
1/4(x-1)+1=2/3(x-1) {去括号}
5/12(x-1)=1 {移项，合并同类项}
x-1=12/5
x=17/5=3.4

Answer 2

1/2(x-1/2(x-1)-1+2)=2/3(x-1)
1/2((x-1)-1/2(x-1)+2)=2/3(x-1)
1/4(x-1)+1=2/3(x-1)
5/12(x-1)=1
x-1=12/5
x=17/5

Answer 3

左边外面的括号打开， 1/2(X-1) - 1/4(X-1) + 1 = 2/3(X-1), 1=(2/3 - 1/4)(X-1)=(5/12)(X-1)
X-1 = 12/5, X= 17/5