\( 2 p < p - q ) \)

It looks like you're working with the inequality: \[ 2p < p - q \] Let's solve this inequality step by step. You can solve for either \( p \) or \( q \). Below are both approaches: ### Solving for \( p \): 1. **Start with the original inequality:** \[ 2p < p - q \] 2. **Subtract \( p \) from both sides to isolate terms containing \( p \):** \[ 2p - p < -q \] \[ p < -q \] **Solution:** \[ p < -q \] ### Solving for \( q \): 1. **Start with the original inequality:** \[ 2p < p - q \] 2. **Subtract \( p \) from both sides to move \( p \) to one side:** \[ 2p - p < -q \] \[ p < -q \] 3. **Multiply both sides by \( -1 \) to solve for \( q \). Remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign:** \[ -p > q \] \[ q < -p \] **Solution:** \[ q < -p \] ### Summary - **Solving for \( p \):** \[ p < -q \] - **Solving for \( q \):** \[ q < -p \] **Interpretation:** The inequality establishes a relationship between \( p \) and \( q \), indicating that \( p \) must be less than the negative of \( q \), and vice versa. If you have any further questions or need additional clarification, feel free to ask!