The problem asks us to compare two numbers: $-6.9$ and $-\sqrt{42}$. We need to determine whether $-6.9$ is less than, greater than, or equal to $-\sqrt{42}$.

1. Problem Description

The problem asks us to compare two numbers: $-6.9$ and $-\sqrt{42}$. We need to determine whether $-6.9$ is less than, greater than, or equal to $-\sqrt{42}$.

2. Solution Steps

First, we can approximate the value of $\sqrt{42}$. Since $6^2 = 36$ and $7^2 = 49$, we know that $\sqrt{36} = 6$ and $\sqrt{49} = 7$. Thus $\sqrt{42}$ is between 6 and

7. Using a calculator, we find that $\sqrt{42} \approx 6.48$.

Therefore, $-\sqrt{42} \approx -6.48$.

Now we compare $-6.9$ and $-6.48$. Remember that with negative numbers, the number with the larger absolute value is actually smaller.

Since $6.9 > 6.48$, we have $-6.9 < -6.48$.

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

3. Final Answer

$-6.9 < -\sqrt{42}$