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

Since E is the midpoint between D and F, we can set up an equation using the midpoint formula. According to the formula, the sum of the distances from E to D and E to F should be equal. So, DE + EF = DF. Substituting the given values, we get (3x + 2) + 18 = 5x. Simplifying the equation, we have 3x + 20 = 5x. By subtracting 3x from both sides, we get 20 = 2x. Dividing both sides by 2, we find x = 10. Therefore, the value of x is 10.