Solve for p.

Question

p–1+2p>11 or 4p+5+15p<5
Write your answer as a compound inequality with integers.

Answer 1

To solve the inequalities \( p - 1 + 2p > 11 \) and \( 4p + 5 + 15p < 5 \), we'll solve each inequality separately and then combine the results.

1. Solve the first inequality: \[ p - 1 + 2p > 11 \] Combine like terms: \[ 3p - 1 > 11 \] Add 1 to both sides: \[ 3p > 12 \] Divide by 3: \[ p > 4 \]

2. Solve the second inequality: \[ 4p + 5 + 15p < 5 \] Combine like terms: \[ 19p + 5 < 5 \] Subtract 5 from both sides: \[ 19p < 0 \] Divide by 19: \[ p < 0 \]

Now, we combine the results. The solution is: \[ p > 4 \quad \text{or} \quad p < 0 \]

Thus, in terms of compound inequalities: \[ (-\infty, 0) \cup (4, \infty) \]

The final answer with integers is: \[ p < 0 \quad \text{or} \quad p > 4 \]