Which of the following is a solution to the inequality below? \[ \begin{array}{l}-5+\frac{126}{v}<3 \\ \qquad v=2 \\ v=7 \\ v=-7\end{array} \]

To solve the inequality \(-5+\frac{126}{v}<3\), we first isolate \(\frac{126}{v}\): \[ \frac{126}{v} < 3 + 5 \] \[ \frac{126}{v} < 8 \] Next, we multiply both sides by \(v\) (keeping in mind that if \(v\) is negative, the inequality sign flips): \[ 126 < 8v \] Now, dividing both sides by 8 gives: \[ \frac{126}{8} < v \] \[ v > 15.75 \] Now let's test the given values: 1. For \(v = 2\): \[ -5 + \frac{126}{2} = -5 + 63 = 58 \quad (\text{not a solution}) \] 2. For \(v = 7\): \[ -5 + \frac{126}{7} = -5 + 18 = 13 \quad (\text{not a solution}) \] 3. For \(v = -7\): \[ -5 + \frac{126}{-7} = -5 - 18 = -23 \quad (\text{a valid solution since it is less than 3}) \] Thus, the only solution to the inequality is \(v = -7\).