The equation given is:

$\frac{2x - 1}{4} + \frac{x}{3} = 2$

Step-by-step solution:

1. Find the least common denominator (LCD): The denominators are $4$ and $3$. The LCD is $12$.

2. Eliminate the denominators by multiplying through by $12$: Multiply every term in the equation by $12$: $12 \cdot \frac{2x - 1}{4} + 12 \cdot \frac{x}{3} = 12 \cdot 2$

   Simplify each term: $3(2x - 1) + 4x = 24$

3. Expand the terms: Expand $3(2x - 1)$: $6x - 3 + 4x = 24$

4. Combine like terms: $10x - 3 = 24$

5. Solve for $x$: Add $3$ to both sides: $10x = 27$

   Divide both sides by $10$: $x = \frac{27}{10} \quad \text{or} \quad x = 2.7$

Final Answer:

$x = \frac{27}{10} \quad \text{or} \quad x = 2.7$

Would you like me to explain any step in more detail? Here are some related questions to expand on this:

1. How do you find the least common denominator for more complex equations?
2. Can this type of equation be solved using substitution instead of clearing the fractions?
3. What are some practical applications of solving linear equations like this?
4. How would the solution change if a negative coefficient were introduced?
5. Could you graph the equation and confirm the solution visually?

Tip: Always check your solution by substituting the value of $x$ back into the original equation.