Final answer:
The value of x must be 3 for ABCD to be a rhombus, which can be determined by setting AB equal to BC and solving the equation x = 2x - 3.
Step-by-step explanation:
To determine the value of x so that ABCD is a rhombus, given that AB = x and BC = 2x - 3, we have to use the property that in a rhombus all sides are equal in length. Since the opposite sides are already equal, we set AB equal to BC to find the value of x.
Therefore, we have the equation:
AB = BC
x = 2x - 3
To solve for x, we subtract x from both sides:
x - x = (2x - 3) - x
0= x - 3
Add 3 to both sides to get:
3 = x
Hence, the value of x must be 3 for ABCD to be a rhombus.