The diagonals of a parallelogram intersect at their midpoint. Then:
[tex]CT=TE[/tex]
Substitute the expressions for each segment and solve for x:
[tex]\begin{gathered} \Rightarrow x+3=2x-6 \\ \Rightarrow x-2x=-6-3 \\ \Rightarrow-x=-9 \\ \Rightarrow x=9 \end{gathered}[/tex]
On the other hand, CE=CT+TE. Substitute the expressions for each segment and the value of x to find the length of CE:
[tex]\begin{gathered} CE=CT+TE \\ =x+3+2x-6 \\ =3x-3 \\ =3(9)-3 \\ =27-3 \\ =24 \end{gathered}[/tex]
Therefore, the length of the segment CE is:
[tex]24[/tex]
