BBA-DBE Bangalore: AlgebraInequalities. Free, no login required.

A company produces rectangular advertising boards such that the width is always at least 8 cm shorter than the length, and both the length and width are integers. If the area of a board cannot be more than $320\text{ cm}^2$ and the width is $x$ cm, then find the maximum possible value of $x$.

A pair of consecutive odd positive integers, both of which are smaller than 19, have a sum that is more than 22. How many such pairs will be there, if we allow a number to be in more than one pair?

Find the sum of the smallest value and the greatest value of $x$ that satisfy the inequality $|5x + 5| - 8 \leq 17$.