Final answer:
The value of x is found to be 11 by using the segment addition postulate and algebra to solve the equation derived from the given segment lengths.
Step-by-step explanation:
The question pertains to the segment addition postulate in geometry, where point B is between points E and D, and the lengths of the segments are given in terms of x. According to the given information: EB = x, BD = x + 9, and ED = 31. To solve for x, the lengths of EB and BD add up to ED, hence we will set up the equation x + (x + 9) = 31 and solve for x.
Step 1: Write the equation based on the segment addition postulate.
Step 2: Combine like terms.
Step 3: Solve for x by subtracting 9 from both sides of the equation.
Step 4: Divide both sides of the equation by 2.
Solution:
- x + (x + 9) = 31
- 2x + 9 = 31
- 2x = 22
- x = 11
Therefore, the value of x is 11.