The equation in the image is:

$\frac{3(x - 1)}{4} = \frac{3(x + 5)}{10}$

To solve for $x$, let's first cross-multiply:

$3(x - 1) \cdot 10 = 3(x + 5) \cdot 4$

Simplify both sides:

$30(x - 1) = 12(x + 5)$

Now, expand both sides:

$30x - 30 = 12x + 60$

Next, we'll isolate $x$ by moving all $x$-terms to one side and constants to the other:

$30x - 12x = 60 + 30$

Simplify:

$18x = 90$

Now, solve for $x$:

$x = \frac{90}{18} = 5$

Solution:

The value of $x$ is 5.

Would you like more details on this solution, or do you have any questions?

Follow-up Questions:

1. How would you solve this equation if the fractions had different coefficients?
2. What happens if you have an equation with more variables?
3. Can you solve similar equations with a different method, such as substitution?
4. How would this change if the terms were squared?
5. How do you check if your solution is correct in this context?

Tip: Always cross-multiply when dealing with equations involving fractions to simplify the process.