Question

初一数学问题，求详解，谢谢

已知关于X的二分之一(1-X)=1+K方程的解与四分之三(X-1)-五分之二(3X+2)=十分之K-二分之3(X-1)的解互为相反数,求K

Answer 1

解：∵1/2(1-x)=1+k
∴1-x=2+2k
x=-2k-1
∵3/4(x-1)-2/5(3x+2)=k/10-3/2(x-1)
∴15(x-1)-8(3x+2)=2k-30(x-1)
15x-15-24x-16=2k-30x+30
21x=61+2k
x=(61+2k)/21
∵解互为相反数
∴-2k-1+(61+2k)/21=0
-42k-21+61+2k=0
40k=40
∴k=1

Answer 2

解方程得
x=-2K-1
x=(2K+43)/23
(-2K-1)+((2K+43)/23)=0
-46K-23+2K+43=0
20=44K
K=5/11