To solve the equation [tex]\(-5x = 4\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Here is a step-by-step process of how we solve it, emphasizing the property of equality used at each step.
1. Given Equation:
[tex]\[
-5x = 4
\][/tex]
2. Isolating the Variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to undo the multiplication of [tex]\(-5\)[/tex] with [tex]\(x\)[/tex]. This can be done by dividing both sides of the equation by [tex]\(-5\)[/tex].
3. Applying the Division Property of Equality:
We divide both sides by [tex]\(-5\)[/tex]:
[tex]\[
\frac{-5x}{-5} = \frac{4}{-5}
\][/tex]
4. Simplifying:
[tex]\[
x = -\frac{4}{5}
\][/tex]
The property of equality used in this solution is the division property of equality. This property 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.
