The interval method is based on the property that a continuous function can only change its sign (from positive to negative or vice versa) by passing through zero. By identifying these "zeros" and marking them on a number line, we divide the line into intervals where the expression maintains a constant sign. 2. General Algorithm for Solving Inequalities
) or any points from the denominator (since division by zero is undefined). gdz metod intervalov 4x
: Shaded intervals that match the inequality's sign ( >0is greater than 0 −negative Find the zeros : Solve . Using the quadratic formula or factoring, we get . The roots are Mark the points : Place hollow circles at -3negative 3 -1negative 1 on the number line (because the inequality is strict, Test intervals : (positive). (negative). (positive). Final Answer : Since we need values <0is less than 0 , the solution is the interval 4. Common Variations The interval method is based on the property