Solve each inequality. Graph the solution set on number line.

$3p+1\le 7\text{or}2p-9\ge 7$

Properties of inequalities are written in following table:

To simplify given inequality, use subtraction and division property of inequalities. Subtract by same number does not change the sign of inequality. Also divide by same positive number does not reverse the sign of inequality as shown below

$\begin{array}{c}3p+1-1\le 7-1\\ 3p\le 6\\ \frac{3p}{3}\le \frac{6}{3}\\ p\le 2\end{array}$

To simplify given inequality, use addition and division property of inequalities. Add by same number does not change the sign of inequality. Also divide by same positive number does not reverse the sign of inequality as shown below

$\begin{array}{c}2p-9+9\ge 7+9\\ 2p\ge 16\\ \frac{2p}{2}\ge \frac{16}{2}\\ p\ge 8\end{array}$

Thus, solution is $p\le 2\text{or p}\ge \text{8}$

Assolution set of the inequality is all real numbers less than or equal to 2 or greater than or equal to 8

Number line starts from 2 to $-\infty$ and from 8 to $\infty$

Dot on 2 and 8 shows these points are included in the solution set