Solve for x given the diagram and expressions for segment lengths: 2x-1, 2y+1, y-3.

The diagram shows three segments marked with a single tick. This indicates that these three segments have equal lengths. The lengths are given by the expressions $(2x-1)$, $(2y+1)$, and $(y-3)$.
Therefore, we can set up the following equations:

$$2x - 1 = y - 3 \quad \text{(Equation 1)}$$ $$2y + 1 = y - 3 \quad \text{(Equation 2)}$$

Equation 2 only contains the variable $y$, so we can solve it directly:

$$2y + 1 = y - 3$$

Subtract $y$ from both sides of the equation:

$$2y - y + 1 = -3$$ $$y + 1 = -3$$

Subtract 1 from both sides of the equation:

$$y = -3 - 1$$ $$y = -4$$

Now that we have the value of $y$, substitute $y = -4$ into Equation 1:

$$2x - 1 = y - 3$$ $$2x - 1 = (-4) - 3$$ $$2x - 1 = -7$$

Add 1 to both sides of the equation:

$$2x = -7 + 1$$ $$2x = -6$$

Divide by 2:

$$x = \frac{-6}{2}$$ $$x = -3$$

The value of $x$ is $\boxed{-3}$.