Since E is a point between D and F, then, we can write an equation that follows:
[tex]DE+EF=DF[/tex]
Replace with the corresponding expressions,
[tex](4x+12)+(7x-9)=(13x-11)[/tex]
group terms that are alike,
[tex]11x+3=13x-11[/tex]
solve for x,
[tex]\begin{gathered} 11x-13x=-11-3 \\ -2x=-14 \\ x=\frac{-14}{-2} \\ x=7 \end{gathered}[/tex]
then, replace x in the expressions DE and EF,
[tex]\begin{gathered} DE=4x+12 \\ DE=4(7)+12 \\ DE=28+12 \\ DE=40 \\ \\ EF=7x-9 \\ EF=7(7)-9 \\ EF=49-9 \\ EF=40 \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} 1.\text{ }x=7 \\ 2.\text{ }DE=40 \\ 3.\text{ }EF=40 \end{gathered}[/tex]
