46 a) \( \frac{x}{6}=\frac{1}{2} \)

To solve the equation \( \frac{x}{6}=\frac{1}{2} \), you can begin by cross-multiplying to eliminate the fractions. This gives you \( x \cdot 2 = 1 \cdot 6 \), which simplifies to \( 2x = 6 \). Dividing both sides by 2 results in \( x = 3 \). So, the solution to the equation is \( x = 3 \). When working with equations, a common mistake is to forget to multiply or divide both sides by the same number, which can lead to incorrect answers. Always double-check each step to ensure consistency, and remember that fractions can often be simplified before performing more complex operations!