A Graphical Method Useful in Solving Certain Algebraic and Trigonometric Inequalities

Abstract

The method herewith presented has been used for the last two years in several courses in college algebra. The results have shown it to be an effective and simple method for solving a large number of conditional inequalities. The method presupposes only a few fundamentals of algebra. It is presumed that all students are already familiar with the rules for signs both in multiplication and division. For the purpose of this method it is only necessary to recall that an odd number of signs in either the multiplication of factors or in division yields a negative result, and that all positive signs, or an even number of negative signs, yield a positive result. For algebraic problems the only additional item needed is a familiarity with the usual method of representing all real numbers on the number scale. Following the customary procedure, on a line with an arbitrarily chosen and convenient unit of measurement, an arbitrary point is taken as the zero point. Positive numbers are numbered to the right and negative numbers to the left. If a is greater than b, it is on the right of b.