To solve the inequality 7n + 1 > 169, we need to isolate the variable n by subtracting 1 from both sides:
7n > 169 - 1
7n > 168
Now, divide both sides of the inequality by 7:
n > 168/7
n > 24
Therefore, the solution to the inequality is n > 24.
To graph this solution on a number line, we represent all the numbers greater than 24 with an open circle at 24 and a shaded region extending to the right.