Final answer:
To find the value of EF, substitute the given expressions for DE and DF into the equation DE + EF = DF. Solve for x, and then substitute x into the expression for EF to find its value.
Step-by-step explanation:
To find the value of EF, we need to solve for x in the equation EF = 2x - 1. Given the information DE = 5x + 5 and DF = 10x - 2, we can set up the equation DE + EF = DF and substitute the expressions for DE, EF, and DF. This gives us (5x + 5) + (2x - 1) = 10x - 2. Simplifying and solving for x, we get x = 2. Substituting x = 2 into the expression for EF, we find EF = 2(2) - 1 = 3. Therefore, the value of EF is 3.