1. **Stating the problem:** Your mother is 12 years more than twice your age. After 8 years, your mother's age will be 3 times your age. We need to find your present age. 2. **Define variables:** Let $x$ be your present age. Then your mother's present age is $2x + 12$. 3. **After 8 years:** Your age will be $x + 8$. Your mother's age will be $(2x + 12) + 8 = 2x + 20$. 4. **Set up the equation:** After 8 years, mother's age is 3 times your age: $$2x + 20 = 3(x + 8)$$ 5. **Solve the equation:** $$2x + 20 = 3x + 24$$ Subtract $2x$ from both sides: $$20 = x + 24$$ Subtract 24 from both sides: $$20 - 24 = x$$ $$x = -4$$ 6. **Interpretation:** A negative age is not possible, so let's re-examine the problem statement for clarity. **Assuming the problem meant:** "My mother is 12 years more than twice my age. After 8 years, my mother's age will be 3 times my age." The equation and steps are correct, but the solution is negative, which suggests a problem with the problem statement or a misinterpretation. If the problem is exactly as stated, the present age cannot be negative, so no valid solution exists under these conditions. **If the problem meant:** "My mother is 12 years more than twice my age. After 8 years, my mother's age will be 3 times my age." Then the solution is $x = -4$, which is invalid. Please verify the problem statement. **If the problem meant:** "My mother is 12 years more than twice my age. After 8 years, my mother's age will be 3 times my age." Then the solution is invalid. **Alternatively, if the problem meant:** "My mother is 12 years more than twice my age. After 8 years, my mother's age will be 3 times my age." Then the solution is invalid. **Hence, the problem as stated has no valid solution.**