To solve the equation [tex]\(-5x = 4\)[/tex], we want to isolate the variable [tex]\(x\)[/tex]. Here's a step-by-step explanation:
1. The original equation is:
[tex]\[
-5x = 4
\][/tex]
2. To isolate [tex]\(x\)[/tex], we need to undo the multiplication of [tex]\(x\)[/tex] by [tex]\(-5\)[/tex]. We can do this by dividing both sides of the equation by [tex]\(-5\)[/tex].
3. Performing the division gives us:
[tex]\[
\frac{-5x}{-5} = \frac{4}{-5}
\][/tex]
4. Simplifying the left side of the equation, we get:
[tex]\[
x = -\frac{4}{5}
\][/tex]
The property of equality used in this process is the division property of equality, which states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.
Therefore, the correct answer is:
D. division property of equality
