The problem asks to identify which of the given equations are equivalent to the equation $-51 = u - v$.

1. Problem Description

The problem asks to identify which of the given equations are equivalent to the equation $-51 = u - v$.

2. Solution Steps

We need to check each equation to see if it is equivalent to $-51 = u - v$.

Equation 1: $17 = \frac{u - v}{-3}$

Multiply both sides by $-3$:

$17(-3) = \frac{u - v}{-3}(-3)$

$-51 = u - v$

This equation is equivalent.

Equation 2: $-17 = \frac{u - v}{3}$

Multiply both sides by $3$:

$-17(3) = \frac{u - v}{3}(3)$

$-51 = u - v$

This equation is equivalent.

Equation 3: $-3 = \frac{u - v}{17}$

Multiply both sides by $17$:

$-3(17) = \frac{u - v}{17}(17)$

$-51 = u - v$

This equation is equivalent.

Equation 4: $3 = \frac{u - v}{-17}$

Multiply both sides by $-17$:

$3(-17) = \frac{u - v}{-17}(-17)$

$-51 = u - v$

This equation is equivalent.

3. Final Answer

All four equations are equivalent to $-51 = u - v$.

$17 = \frac{u - v}{-3}$

$-17 = \frac{u - v}{3}$

$-3 = \frac{u - v}{17}$

$3 = \frac{u - v}{-17}$