DE and EF are segments of the line DF, so they will add up to DF. This can be represented with this equation:
[tex] (4x + 10) + (2x - 1) = 9x - 15 [/tex]
Combine like terms:
[tex] 4x + 2x = 6x [/tex]
[tex] 10 + (-1) = 9 [/tex]
[tex] 6x + 9 = 9x - 15 [/tex]
Add 15 to both sides:
[tex] 6x + 24 = 9x [/tex]
Subtract 6x from both sides:
[tex] 24 = 3x [/tex]
Divide both sides by 3 to get x by itself:
[tex] \boxed{x = 8} [/tex]
The value of x will be 8.
Plug this value of x into the expression for DF:
[tex] 9(8) - 15 = 72 - 15 = \boxed{57} [/tex]
DF will equal 57.
