Solve the inequality $15 x+1>3(5 x+1)-x+6$ and select the graph of the solutions. What is the solution? $\{x \mid \square$ (Type an inequality.)

Step 1 ：First, simplify the inequality by distributing the 3 on the right side of the inequality and then combining like terms. This gives us the inequality $15x + 1 > 14x + 9$.

Step 2 ：Next, isolate x on one side of the inequality to find the solution. This gives us $x > 8$.

Step 3 ：Finally, represent this solution graphically. The graph is a line graph where the line starts at $x = 8$ and continues to the right, indicating that all values greater than 8 are part of the solution.

Step 4 ：\(\boxed{x > 8}\) is the solution to the inequality $15x + 1 > 3(5x + 1) - x + 6$.