Solving Rational Inequalities

Front

What is a rational inequality?

Back

A rational inequality is an inequality that involves a rational expression, which is a fraction where the numerator and denominator are polynomials.

Front

How do you solve a rational inequality?

Back

To solve a rational inequality, you first find the critical points by setting the numerator and denominator to zero, then test intervals between these points to determine where the inequality holds true.

Front

What does the notation 'u' represent in interval notation?

Back

The notation 'u' represents the union of two sets, indicating that the solution includes all values from both intervals.

Front

What is the significance of critical points in solving rational inequalities?

Back

Critical points are the values where the rational expression is either zero or undefined, and they help to divide the number line into intervals for testing.

Front

What does the interval notation (-∞, -2) mean?

Back

The interval notation (-∞, -2) represents all real numbers less than -2.

Front

What does the interval notation [1, ∞) mean?

Back

The interval notation [1, ∞) represents all real numbers greater than or equal to 1.

Front

How do you determine the sign of a rational expression in an interval?

Back

To determine the sign of a rational expression in an interval, choose a test point from the interval and substitute it into the expression to see if the result is positive or negative.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Front

What does the solution set of a rational inequality represent?

Back

The solution set of a rational inequality represents all the values of the variable that satisfy the inequality.

Front

What is the importance of graphing rational inequalities?

Back

Graphing rational inequalities helps visualize the solution set and understand where the inequality holds true on the number line.