This image presents two similar triangles, and the problem asks to solve for $x$.

Since the triangles are similar, we can set up a proportion between the corresponding sides of the two triangles.

The sides corresponding to each other are:

• The larger triangle has sides 6 and $x-1$, while the smaller triangle has sides 3 and 2.

We can write the proportion as: $\frac{6}{3} = \frac{x-1}{2}$

Now, let's solve for $x$:

$\frac{6}{3} = 2 \quad \text{(since } 6 \div 3 = 2)$ $2 = \frac{x-1}{2}$ Now multiply both sides by 2 to eliminate the denominator: $4 = x - 1$ Add 1 to both sides: $x = 5$

Thus, $x = 5$.

Would you like further details or have any questions?

Here are 5 related questions to explore this further:

1. How do we determine if two triangles are similar?
2. What is the importance of proportions in solving problems involving similar triangles?
3. What other geometric properties can be derived from similar triangles?
4. How can you verify if your solution for $x$ is correct?
5. What happens if one of the sides was given as a variable instead of a constant?

Tip: When dealing with similar triangles, always ensure that corresponding sides are correctly identified before setting up a proportion.