Find the length of the mid segment. the diagram is not to scale.

for my initial answer i got

i did, 2(6x + 4) = 4x + 56, and then x = 6
plug it in to get 40

can someone check my work : ) you so much

You have the correct x value and correct midsegment length. You're on a roll.

To check your answer, simply replace every copy of x with 6 and then simplify each side

2*(6*x+4) = 4*x+56
2*(6*6+4) = 4*6+56 ... replace every x with 6
2*(36+4) = 24+56
2*40 = 80
80 = 80 
The last equation is true so the first equation is true when x = 6
The answer has been confirmed.

Once you know x = 6, the rest of the problem isn't too bad
6*x+4 = 6*6+4 = 36+4 = 40
which is what you got. So that part is correct as well

Or you can compute the bottom side
4*x+56 = 4*6+56 = 24+56 = 80
and then cut that in half
80*(1/2) = 40

Either way the midsegment is 40 units long.