For what value of k will the two equations -x+k=2x-1 and 2x+4=4(x-2) have the same solution?

We'll determine the solution of the equation whose
coefficients are determined and we'll impose the constraint that the found solution to
be the solution of the equation that contains k.

We'll
solve the equation
2x+4=4(x-2):

2x+4=4(x-2)

We'll
divide by 2 both sides:

x + 2 =
2(x-2)

We'll move all terms to one
side:

x + 2 - 2(x-2) = 0

We'll
remove the brackets:

x + 2 - 2x + 4 =
0

We'll combine like terms:

-x
+ 6 = 0

-x = -6

x =
6

We'll impose the constraint that x = 6 to be the solution
of the equation -x+k=2x-1.

That means that the x=6 has to
verify the equation.

-6 + k = 12 -
1

-6 + k = 11

k = 11 +
6

k = 17

The
value of k for the given equations to have the same solution is k =
17.