Final answer:
To find the value of x, we can use the segment addition property and solve the equation 4x + 8 = 9x - 22.
Step-by-step explanation:
To find the value of x, we can use the segment addition property. According to the property, the sum of the lengths of two parts of a segment is equal to the length of the whole segment. In this case, we have DE + EF = DF.
Substituting the given values, we get (4x-1) + 9 = 9x-22. Now we can solve this equation for x.
Combining like terms, we have 4x + 8 = 9x - 22. Subtracting 4x from both sides, we get 8 = 5x - 22. Adding 22 to both sides, we get 30 = 5x. Finally, dividing both sides by 5, we get x = 6.