Let's solve the given equation step-by-step to identify which property of equality was used:
1. Given the equation:
[tex]\[
-5x = 4
\][/tex]
2. To isolate [tex]\( x \)[/tex], we need to divide both sides of the equation by [tex]\( -5 \)[/tex]:
[tex]\[
\frac{-5x}{-5} = \frac{4}{-5}
\][/tex]
3. Simplifying both sides, we get:
[tex]\[
x = -\frac{4}{5}
\][/tex]
The key step here was dividing both sides of the equation by [tex]\( -5 \)[/tex]. The property of equality that allows us to divide both sides by the same nonzero number while keeping the equation balanced is known as the Division Property of Equality.
Therefore, the correct answer is:
[tex]\[
\text{D. division property of equality}
\][/tex]
