1. **Stating the problem:** We are given an L-shaped figure with a horizontal segment labeled $x - 1$ and a vertical segment labeled $x$. The height of the vertical segment is 2, and the height of the short vertical left segment is 1. We want to find the value of $x$. 2. **Understanding the figure:** The total height of the vertical segment is 2, which is composed of the short vertical segment of height 1 plus the vertical segment labeled $x$. Therefore, we can write the equation: $$1 + x = 2$$ 3. **Solving the equation:** $$1 + x = 2$$ Subtract 1 from both sides: $$\cancel{1} + x = 2 - \cancel{1}$$ which simplifies to: $$x = 1$$ 4. **Conclusion:** The value of $x$ is 1. This means the horizontal segment labeled $x - 1$ is: $$x - 1 = 1 - 1 = 0$$ which fits the L-shape where the horizontal segment length is zero at this value.