The midpoint of u is in the middle of t and v. T is 3x+9 and v is 14+2x. what is Tu, tv, and uv?

TV = 3x+9 - (14+2x)

TV = 3x + 9 -14 - 2x

TV = x - 5

U = ((3x + 9) + (14 + 2x)) / 2

U = (5x + 23) / 2

TU = (2(3x + 9) / 2) - (5x+23)/2

TU = (6x + 18 - 5x -23) /2

TU = (x - 5) / 2

Since U is the midpt, UV = TU, so UV = (x-5) / 2

TU + UV = TV

(x-5) / 2 + (x-5) /2 = 2 (x-5) /2 = x-5 = TV

Use a number for x. Let's use 10.

T is 39, V = 34

U = (39 + 34)/2 = 73/2 = 36.5

TV = 39-34 = 5

TV from our equation is x-5. 10 - 5 = 5. Good.

TU and UV = (x-5) / 2. (10-5) /2 = 5/2.

(39-34)/2 = 5/2 Good.