To solve the equation [tex]\(-\frac{4}{5} x = 80\)[/tex] for [tex]\(x\)[/tex] in one step, we need to eliminate the coefficient of [tex]\(x\)[/tex] on the left-hand side of the equation.
The coefficient of [tex]\(x\)[/tex] is [tex]\(-\frac{4}{5}\)[/tex]. To isolate [tex]\(x\)[/tex], we multiply both sides of the equation by the reciprocal of [tex]\(-\frac{4}{5}\)[/tex].
The reciprocal of [tex]\(-\frac{4}{5}\)[/tex] is [tex]\(-\frac{5}{4}\)[/tex].
So, we multiply both sides of the equation by [tex]\(-\frac{5}{4}\)[/tex]:
[tex]\[
-\frac{4}{5} \left(-\frac{5}{4}\right) x = 80 \left(-\frac{5}{4}\right)
\][/tex]
This simplifies as follows:
[tex]\[
(-\frac{4}{5}) \times (-\frac{5}{4}) = 1
\][/tex]
Thus, the left-hand side simplifies to [tex]\(x\)[/tex]:
[tex]\[
x = 80 \times (-\frac{5}{4})
\][/tex]
Therefore, after computing the right-hand side:
[tex]\[
x = -100
\][/tex]
Thus, the correct one-step way to solve the equation is:
[tex]\[
-\frac{4}{5}\left(-\frac{5}{4}\right) x=80\left(-\frac{5}{4}\right)
\][/tex]
