Final answer:
In general, we can determine whether a number is even or odd by looking at its last digit. If the last digit is even (0, 2, 4, 6, or 8), then the number is even. If the last digit is odd (1, 3, 5, 7, or 9), then the number is odd. Therefore, x is even if and only if 3x^5 is odd.
Step-by-step explanation:
In general, we can determine whether a number is even or odd by looking at its last digit. If the last digit is even (0, 2, 4, 6, or 8), then the number is even. If the last digit is odd (1, 3, 5, 7, or 9), then the number is odd. Let's consider the equation y = 3x^5x. We can break this down into two parts: 3x^5 and x.
If x is even, then the last digit of x will be even. Since the last digit of x is even, the last digit of 3x^5 will also be even. Therefore, 3x^5 is odd. If x is odd, then the last digit of x will be odd. Since the last digit of x is odd, the last digit of 3x^5 will also be odd. Therefore, 3x^5 is odd. So, we have shown that x is even if and only if 3x^5 is odd.