Final answer:
To solve for x in the given rhombus problem, we can use the properties of a rhombus and set up an equation based on the given information. By combining like terms and isolating x, we find that x = 1/2.
Step-by-step explanation:
To solve for x in the given problem, we need to use the properties of a rhombus and apply them to the given information. In a rhombus, the diagonals are perpendicular bisectors of each other.
Since PR and QS are diagonals of the rhombus, they are also perpendicular bisectors. Therefore, we can set up the following equation:
PQ = 6x + 1 = QR = 5 - 2x
Simplifying this equation gives us:
6x + 1 = 5 - 2x
Now, we can solve for x by combining like terms and isolating x:
6x + 2x = 5 - 1
8x = 4
x = 4/8
x = 1/2
Therefore, x = 1/2.