Solve the following inequality and graph the solution set on a number line. \[ 5(x+1)-9<4 x+1 \] What is the solution set? $\{x \mid$ (Type an inequality.)

Step 1 ：First, we need to simplify the inequality by distributing the 5 on the left side and then moving all terms to one side of the inequality. This will give us a simpler inequality that we can solve for x.

Step 2 ：The simplified inequality is \(x < 5\). Now we need to graph this inequality on a number line.

Step 3 ：Final Answer: The solution set for the inequality \(5(x+1)-9<4x+1\) is \(\boxed{x<5}\).