In Figure, `R E N T` is a rectangle. Its diagonals meet at `Odot` Find `x,` if `O R=2x+4\ a n d\ O T=3x+1.`

Explanation

To solve the problem, we need to find the value of \( x \) given that \( OR = 2x + 4 \) and \( OT = 3x + 1 \) in rectangle \( RENT \) where the diagonals intersect at point \( O \).

### Step-by-Step Solution:

1. **Understand the properties of a rectangle**: In a rectangle, the diagonals bisect each other. This means that the segments from the center of the rectangle to the vertices are equal. Therefore, we can say that \( OR = OT \).

2. **Set up the equation**: Since \( OR \) and \( OT \) are equal, we can set the expressions for \( OR \) and \( OT \) equal to each other:
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