Final answer:
To find the value of x when A is the midpoint of DB, we set the length of AB equal to half the length of DB and solve for x. After solving the equation, the value of x is 12, which is not listed among the provided options, indicating a possible typo in the question or options.
Step-by-step explanation:
If A is the midpoint of DB, then segment DA is congruent to segment AB. Therefore, the lengths of DA and AB are equal. Given that the entire length of DB is (6x−18) and AB is (2x+3), we can set up the equation (2x+3) = (6x−18)/2.
Let's solve for x:
Multiply both sides by 2 to eliminate the fraction: 2*(2x+3) = 6x−18.
This gives us 4x + 6 = 6x - 18.
Subtract 4x from both sides: 6 = 2x - 18.
Add 18 to both sides: 24 = 2x.
Divide both sides by 2: x = 12.
The value of x that satisfies the equation is 12. However, since 12 is not one of the provided options, it seems there might have been a typo in the provided options or in the original equations given in the question. Please double-check the data provided.