To solve the equation using the cross-multiplication property, let's start with the given proportion:

$\frac{1}{2} = \frac{2x - 1}{3}$

Using cross-multiplication, we multiply the numerator of each side by the denominator of the other side:

$1 \cdot 3 = 2 \cdot (2x - 1)$

This simplifies to:

$3 = 4x - 2$

Next, we'll add 2 to both sides to isolate terms involving $x$:

$3 + 2 = 4x$

$5 = 4x$

Now, divide both sides by 4 to solve for $x$:

$x = \frac{5}{4}$

So, the solution is:

$x = \frac{5}{4}$

Would you like further details on this solution or have any questions?

Here are 5 related questions that might deepen your understanding:

1. What is the cross-multiplication property, and why does it work?
2. How can we verify if the solution $x = \frac{5}{4}$ is correct?
3. What would change if the terms in the proportion were different?
4. Are there alternative methods to solve this proportion without cross-multiplication?
5. Can you use cross-multiplication on equations that are not set up as proportions?

Tip: When working with proportions, remember to check that the denominators are non-zero before using cross-multiplication.