a$)$ Evaluate the inequality $9$n $-13<=2$n for values of n from $0$ up to $7.$ That mean calculate each side for the given value of n$,$ then say whether the inequality is true or false.

b$)$ Consider that statement $"9$n $-13<=2$n for all n $>=\_\_\_\_\_\_\_\_".$ Fill in the blank with the smallest whole number that appears to make the statement true, i$.$e$.9$n$-13<=2$n is true for that value of n and appears to remain true for bigger values. Justify your answer using the results from Part a$.$

c$)$ Prove the statement in Part b $($with the blank filled in$)$ by induction. To ensure you get credit, use the format I taught you for the inductive step. That means start with the left side of the desired inequality and use a linear chain of expressions linked by $<=$ and $=$ to reach the right side. Be sure to say where the inductive step was used. Also say where you used any fact about k$.$