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

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We need the value of k for which -x+k=2x-1 and 2x+4=4(x-2) have the same solution.

2x + 4 = 4(x - 2)

=> 2x + 4 = 4x - 8

=> 2x = 12

=> x = 6

Substitute x = 6 in -x + k = 2x - 1

=> -6 + k = 2*6 - 1

=> k = 12 + 6 - 1

=> k = 17

**The required value is k = 17**

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 theĀ given equations to have the same solution is k = 17.**