To solve the equation:

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

Step-by-Step Solution:

1. Eliminate the fractions by finding the least common denominator (LCD): The denominators are 4 and 3. The LCD is $12$. Multiply through by $12$:

   $12 \cdot \frac{2x - 1}{4} + 12 \cdot \frac{x}{3} = 12 \cdot 2$

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

3. Expand the terms: $6x - 3 + 4x = 24$

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

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

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

Final Answer:

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

Would you like further clarification on any step or additional examples?

Related Questions:

1. What are the general steps to solve equations involving fractions?
2. How do you find the least common denominator (LCD) of two numbers?
3. What strategies are useful when simplifying algebraic expressions?
4. Can you explain how to verify the solution to this equation?
5. How are similar equations used in real-world problem solving?

Tip:

Always verify your solution by substituting the value of $x$ back into the original equation to ensure the equality holds.