Solve the inequality. Write the solution set in interval notation, and graph it. \[ 16<7 p+2<37 \] The solution set is

To solve the inequality \( 16 < 7p + 2 < 37 \), follow these steps: 1. **Subtract 2 from all parts of the inequality:** \[ 16 - 2 < 7p + 2 - 2 < 37 - 2 \] \[ 14 < 7p < 35 \] 2. **Divide each part by 7 to isolate \( p \):** \[ \frac{14}{7} < p < \frac{35}{7} \] \[ 2 < p < 5 \] 3. **Express the solution in interval notation:** \[ (2, 5) \] 4. **Graphing the Solution:** - Draw a number line. - Place open circles (parentheses) at 2 and 5 to indicate that these endpoints are not included. - Shade the region between 2 and 5 to represent all real numbers \( p \) that satisfy the inequality.  *Graphical Representation of the Solution:* \[ \text{--------(}2\text{)}\ \underline{\hspace{1.5cm}}\ (\!5\text{)--------} \] **Final Answer:** \(\boxed{\, (\,2,\;\!5\,)}\)