The equation provided in the image is:

$\frac{1}{2} \cdot \left(x - \frac{3}{4}\right) = \frac{5}{6}$

Solution:

1. Eliminate the fraction in front of the parentheses by multiplying both sides by $2$: $x - \frac{3}{4} = 2 \cdot \frac{5}{6}$

2. Simplify the right-hand side: $x - \frac{3}{4} = \frac{10}{6}$

3. Simplify $\frac{10}{6}$ to $\frac{5}{3}$: $x - \frac{3}{4} = \frac{5}{3}$

4. Add $\frac{3}{4}$ to both sides to isolate $x$: $x = \frac{5}{3} + \frac{3}{4}$

5. Find a common denominator to add the fractions. The least common denominator (LCD) of 3 and 4 is 12: $x = \frac{20}{12} + \frac{9}{12}$

6. Add the fractions: $x = \frac{29}{12}$

Final Answer:

$x = \frac{29}{12}$

Let me know if you would like further clarification or steps explained!

Here are 5 related questions:

1. What is the process to solve an equation with fractions?
2. How do you find the least common denominator of two fractions?
3. How can you verify your solution for a linear equation?
4. How does distributing fractions differ from distributing integers?
5. What are some alternative methods for solving linear equations with fractions?

Tip: Always simplify fractions as much as possible during calculations to make the process easier!