Finding the Smallest Value When x < 0: Negative Number Comparison

To determine which value is the smallest when $0 > x$, we evaluate each of the given expressions under the assumption that $x$ is negative.

• $-300x$: When a negative number $x$ is multiplied by $-300$, it becomes a large positive number because multiplying two negatives yields a positive. Thus, $-300x$ is a large positive number.
• $-7x$: Similarly, if we multiply $x$ by $-7$, this also results in a positive number, but it will be much smaller than $-300x$ in magnitude because the multiplication factor is much smaller.
• $x + 8$: Adding 8 to a negative number $x$ raises its value towards zero, making it less negative or possibly positive, depending on $x$'s magnitude.
• $x$: As $x$ is a negative number, it remains the smallest among all these expressions. No operation is applied to change its sign or significantly increase its value.

Therefore, among the choices provided, the smallest value is simply $x$ itself because it remains negative and no operation converts it into a positive or larger magnitude value.

The answer is $x$.