Final answer:
After combining like terms and canceling out -7f on both sides of the equation, we find that none of the provided options (A, B, C, D) matches the correct answer, which is -11g.
Step-by-step explanation:
To solve the given algebraic equation 1g - 7f + 3g = 15g - 7f, we first simplify and combine like terms on both sides. On the left-hand side, we combine the terms with g to get 4g - 7f, because 1g + 3g equals 4g. Since the terms -7f appear on both sides, they cancel each other out. Now, we have 4g = 15g after removing the -7f terms.
To isolate g, we subtract 4g from both sides of the equation, resulting in 0g = 11g. Therefore, to solve for g, we subtract 15g from 4g, yielding -11g, which means the correct answer is none of the above options provided in the question.