: Test a value from each interval or use the rule of alternating signs (starting from the rightmost interval).
: 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
To solve a rational inequality, follow these standardized steps: gdz metod intervalov 4x
) or any points from the denominator (since division by zero is undefined).
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 : Test a value from each interval or
: Find the "zeros" by setting the numerator and denominator (if applicable) to zero. Mark Points on a Number Line : Solid dots : Used for non-strict inequalities ( ≤is less than or equal to ≥is greater than or equal to ) for points in the numerator. Hollow (open) dots : Used for strict inequalities ( is greater than
: Move all terms to the left side so the right side is zero, and simplify the expression into a single fraction or product. The roots are Mark the points : Place
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