Question

The equation 2x + 4k − 9 = kx − k + 1 is really a family of equations, because for each value of k, we get a different equation with the unknown x. the letter k is called a parameter for this family. what value should we pick for k to make the given value of x a solution of the resulting equation? (if all real numbers are solutions, enter reals.)

Answer 1

You haven't shared "the given value of x," or, if you have, you haven't drawn attention to it.

Just suppose we were to choose x = 4 as a possible solution and then try to find a value of the parameter k that would make x = 4 an actual solution.

2(4) + 4k - 9 = (4)(4) - (4) + 1

Then 8 + 4k - 9 = 16 - 4 + 1, or       4k - 1 = 13.  Then 4k = 14, and k = 14/4, or (after reduction)  k = 7/2   

If the parameter k equals 7/2, then x = 4 is a solution to the given equation.

To check this out further, start with the proposed solution x = 5 and find k.