Solve the first equation: \(\frac{5x - 3}{4} = \frac{7}{12}\)

Solution:

1. Clear the denominators: Multiply both sides of the equation by the least common multiple of 4 and 12, which is 12. \(12 \cdot \frac{5x - 3}{4} = 12 \cdot \frac{7}{12}\)
2. Simplify: This results in \(3(5x - 3) = 7\).
3. Distribute: Multiply 3 by each term inside the parentheses: \(15x - 9 = 7\).
4. Isolate the term with x: Add 9 to both sides of the equation: \(15x = 7 + 9\), which simplifies to \(15x = 16\).
5. Solve for x: Divide both sides by 15: \(x = \frac{16}{15}\).

Answer: \(x = \frac{16}{15}\)