Question

select all of the equations below that are equivalent to:
\\(\frac{-97}{u} = -28\\)
use properties of equality.
\\(\frac{-97}{-4u} = 6\\) \\(\frac{-97}{14u} = -2\\)
\\(\frac{-97}{u \cdot 7} = 4\\) \\(\frac{-97}{2u} = -15\\)

Explanation:

Step1: Solve original equation for u

Start with $\frac{-97}{u} = -28$. Multiply both sides by $u$: $-97 = -28u$. Divide by $-28$: $u = \frac{97}{28}$.

Step2: Test first option

Substitute $u=\frac{97}{28}$ into $\frac{-97}{-4u}$: $\frac{-97}{-4\times\frac{97}{28}} = \frac{-97}{-\frac{388}{28}} = \frac{-97\times28}{-388} = 7$. This $
eq6$, so not equivalent.

Step3: Test second option

Substitute $u=\frac{97}{28}$ into $\frac{-97}{14u}$: $\frac{-97}{14\times\frac{97}{28}} = \frac{-97}{\frac{1358}{28}} = \frac{-97\times28}{1358} = -2$. This matches, so equivalent.

Step4: Test third option

Substitute $u=\frac{97}{28}$ into $\frac{-97}{u\cdot7}$: $\frac{-97}{\frac{97}{28}\times7} = \frac{-97}{\frac{679}{28}} = \frac{-97\times28}{679} = -4$. This $
eq4$, so not equivalent.

Step5: Test fourth option

Substitute $u=\frac{97}{28}$ into $\frac{-97}{2u}$: $\frac{-97}{2\times\frac{97}{28}} = \frac{-97}{\frac{194}{28}} = \frac{-97\times28}{194} = -14$. This $
eq-15$, so not equivalent.

Answer:

$\frac{-97}{14u} = -2$