Step-by-step explanation:To find \( g(q) \), we need to solve the equation \(-7q + 12r = 3q - 4r\) for \( r \).1. Start with the original equation: \[ -7q + 12r = 3q - 4r \]2. Rearrange the equation by collecting all terms involving \( r \) on one side and \( q \) on the other side: \[ 12r + 4r = 3q + 7q \] This simplifies to: \[ 16r = 10q \]3. Now, divide both sides by 16 to solve for \( r \): \[ r = \frac{10q}{16} \] Simplifying this gives: \[ r = \frac{5q}{8} \]Thus, the function \( g(q) \) can be expressed as:\[g(q) = \frac{5q}{8}