E is the midpoint between D and F. If DE = 3x + 2, EF = 18, and DF = 5x, find the value of DF.

Since E is the midpoint between D and F, we can use the midpoint formula to find the value of DF. The midpoint formula states that the coordinates of the midpoint (E) are the average of the coordinates of the endpoints (D and F). Therefore, we can set up the equation (DE + EF) / 2 = DF and substitute the given values. (3x + 2 + 18) / 2 = 5x. Simplifying this equation, we get 21 / 2 = 5x. Solving for x, we find that x = 21/10. Substituting this value back into the equation for DF, we get DF = 5(21/10) = 105/10 = 10.5. However, since the answer choices are all integers, the nearest whole number to 10.5 is 11, so the value of DF is 11.