It is known that the equation 9x-3 = KX + 14 about X has integer solution. Find the value of all integers K satisfying the condition

It is known that the equation 9x-3 = KX + 14 about X has integer solution. Find the value of all integers K satisfying the condition

9x-3 = KX + 14, (9-k) x = 17, ∵ x, K are all integers, ∵ (9-k), X are all integers, ∵ 9-k = - 17, - 1, 1 or 17, ∵ k = 26, 10, 8, - 8

On the equation kx-4 = 0 of X, the solution is a positive integer and the value of K is obtained

Because x is a positive integer, X ＞ 0
And because kx-4 = 0
So KX = 4
X=4/K
Because x ＞ 0, so 4 / K ＞ 0
So k = 1,2,4

When k takes what value, the equation 9x-3 = KX + 14 related to X has a positive integer solution? Find its positive integer solution

9x-3=kx+14
(9-k)x=17
X = 17 / (9-k) is a positive integer
If K is an integer, then k = 8, - 8
Its positive integer solution: 17,1
(if K is not an integer, there are innumerable)

It is known that the solution of the equation KX = 4-x about X is a positive integer

The original equation is transformed into KX + x = 4, that is, (K + 1) x = 4, the solution of the equation KX = 4-x about X is a positive integer, and the product of K + 1 and X is 4, then K + 1 = 4 or K + 1 = 2 or K + 1 = 1 can be obtained, and the solution is k = 3 or K = 1 or K = 0. Therefore, the integer solution of K can be obtained as 0, 1, 3