We need to compare $-6.9$ and $-\sqrt{42}$ and determine which is greater or if they are equal.

1. Problem Description

We need to compare $-6.9$ and $-\sqrt{42}$ and determine which is greater or if they are equal.

2. Solution Steps

First, let's find the approximate value of $\sqrt{42}$. Since $6^2 = 36$ and $7^2 = 49$, we know that $6 < \sqrt{42} < 7$.

We can estimate $\sqrt{42}$ to be approximately $6.5$ since $42$ is roughly halfway between $36$ and $49$. More precisely, we can use a calculator to find that $\sqrt{42} \approx 6.48$.

Then, we have $-\sqrt{42} \approx -6.48$.

Now we compare $-6.9$ and $-6.48$. Recall that for negative numbers, the number with the smaller absolute value is larger. Since $|-6.9| = 6.9$ and $|-6.48| = 6.48$, we have that $6.9 > 6.48$. Therefore, $-6.9 < -6.48$.

Thus, $-6.9 < -\sqrt{42}$.

3. Final Answer

$-6.9 < -\sqrt{42}$