Inequalities with one unknown

Inequalities of the form ax > b, ax < b, ax ≥ b, ax ≤ b are called linear inequalities with one unknown. A value of the unknown that turns the inequality into a true numerical inequality is its solution; to solve an inequality means to find all its solutions or show that there are none. We use the basic properties: moving a term to the other side with the sign changed gives an equivalent inequality; multiplying or dividing both sides by a positive number keeps the sign; multiplying or dividing by a negative number reverses it. The answer is usually written as an inequality such as x < a or x ≥ a, or as a numerical interval.