\[ \frac{1}{7 b}=\frac{11 x}{y} \] The given equation relates the positive numbers \( b, x \), and \( y \). Which equation correctly expresses \( x \) in terms of \( b \) and \( y \) ? \( x=\frac{y}{77 b} \) \( x=\frac{7 b y}{11} \) \( x=77 b y \) \[ \begin{array}{ll}x=77 b\end{array} \]

To isolate \( x \) from the given equation \( \frac{1}{7b} = \frac{11x}{y} \), you can cross-multiply. This gives you \( y = 77bx \), and then, solving for \( x \) yields \( x = \frac{y}{77b} \). This means \( x \) is directly proportional to \( y \) and inversely proportional to \( b \). If you're working with equations involving variables, always keep an eye on your units or dimensions. A common mistake could be neglecting to consider how changes in one variable affect the others. It's important to double-check each manipulation step to ensure you haven't inadvertently changed the equation's meaning. Thus, remember to verify dimensions and units when applying any transformations!