Inequalities. Interval method

The interval method is a systematic way to solve inequalities involving rational expressions (fractions with polynomials in the numerator and denominator). The main idea is to find the values where the expression is zero or undefined, use these to divide the number line into intervals, and then test the sign of the expression in each interval.

Important properties

• Critical points are where the numerator or denominator is zero.

• The sign of the rational expression can only change at these critical points.

• Test a value from each interval to determine if the expression is positive or negative there.

• Be careful with points where the denominator is zero: these are not included in the solution.