we know the full length DF = 42, hmmm wait a second, but the full length is really the segments DE + EF, namely
[tex]\bf \stackrel{DE}{(7x+1)}~~+~~\stackrel{EF}{(4x-3)}~~=~~\stackrel{DF}{42}\qquad \implies \qquad 11x-2=42 \\\\\\ 11x=44\implies x = \cfrac{44}{11}\implies x = 4 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{DE}{7x+1}\implies 7(4)+1\implies \stackrel{DE}{29}[/tex]
