Finding Maximum Value: Comparing Expressions with x > 0

Video Solution

Solution Steps

00:00 Find the largest value

00:08 The unknown is necessarily positive, and the number is also positive

00:18 However, we don't know if A is positive or negative

00:28 Therefore we cannot know

00:34 The same thing happens here too

00:54 Negative times positive is always negative

01:00 This option is necessarily not the largest

01:05 Therefore we cannot know, and this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll evaluate the expressions based on the condition $0 < x$ :

If $300ax$ is considered, the sign and magnitude depend heavily on $a$ . If $a$ is positive, $300ax$ is large positive. If $a$ is negative, it's large negative.
$\frac{x}{300a}$ is affected by both $x$ and $a$ . If $a$ is positive, this expression shrinks, if $a$ is negative, the sign is inverted, and it becomes positive, but its magnitude determination needs $a$ .
$-2x$ results in a definite negative value because $x$ is positive.

Without knowing the sign or value of $a$ , we can't definitively compare or compute the sizes of the expressions relative to each other.

Therefore, the solution to the problem is: It is not possible to calculate.