The longest side of a triangle is 3 times the shortest side and the third side is 2cm shorter than the longest side. If the perimeter of the triangle is at least 61cm, find the minimum length of the shortest side.

Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.

Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least 5cm longer than the second?

Represent the following inequalities graphically in a two dimensional plane. (1) x + y < 5