1. The problem asks to find the area of the shaded region in the given rectangle. 2. The rectangle is divided into two vertical parts, each with width $x+1$, so the total width is $2(x+1)$. 3. The height of the shaded region is given as $2x - 1$. 4. The formula for the area of a rectangle is $\text{Area} = \text{width} \times \text{height}$. 5. Substitute the values: $$\text{Area} = 2(x+1) \times (2x - 1)$$ 6. Expand the expression: $$= 2(x+1)(2x - 1) = 2[(x)(2x) + (x)(-1) + (1)(2x) + (1)(-1)]$$ $$= 2(2x^2 - x + 2x - 1) = 2(2x^2 + x - 1)$$ 7. Multiply through by 2: $$= 4x^2 + 2x - 2$$ 8. Therefore, the area of the shaded region is: $$\boxed{4x^2 + 2x - 2}$$