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

1. Problem Description

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

2. Solution Steps

First, let's manipulate the original equation $-51 = u - v$.

Multiplying both sides by -1:

$(-1) * (-51) = (-1) * (u - v)$

$51 = -u + v$

$51 = v - u$

Now, let's check each of the given options:

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

Multiplying both sides by -3:

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

$-51 = u - v$

This matches the original equation. So, this is a correct option.

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

Multiplying both sides by 3:

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

$-51 = u - v$

This matches the original equation. So, this is a correct option.

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

Multiplying both sides by 17:

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

$-51 = u - v$

This matches the original equation. So, this is a correct option.

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

Multiplying both sides by -17:

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

$-51 = u - v$

This matches the original equation. So, this is a correct option.

3. Final Answer

All of the options are equivalent to the original equation.

The equivalent equations are:

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

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

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

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