Rational Inequalities and Their Solutions

This video tutorial explains how to solve a rational inequality by transforming it into a form that can be compared to zero. It covers adding fractions, simplifying expressions, factoring, and finding zeros. The tutorial also demonstrates plotting these zeros on a number line, testing intervals, and determining the solution using interval notation. Finally, it shows how to verify the solution using a graphing calculator.

What is the first step in solving a rational inequality that is not in the form of a rational expression compared to zero?

• Subtract a constant from both sides

• Add a constant to both sides

• Divide both sides by a variable

• Multiply both sides by zero

When adding fractions in a rational inequality, what is necessary to perform the addition?

• A common numerator

• A common denominator

• A common variable

• A common constant

What is the common factor in the numerator of the expression 3x + 9?

• 6

• 3

• 2

• 1

How do you determine the zeros of the numerator in a rational inequality?

• Set the numerator equal to zero

• Set the entire expression equal to zero

• Set the numerator greater than zero

• Set the denominator equal to zero

What type of points are used on the number line for zeros of the denominator?

• Dashed points

• Solid points

• Open points

• Closed points

Which interval is part of the solution if the test point results in a positive value?

• The interval to the left of the test point

• The interval to the right of the test point

• The interval containing the test point

• The interval excluding the test point

In interval notation, how is the solution represented if it extends to negative infinity?

• With an open bracket

• With a closed bracket

• With a parenthesis

• With a curly brace

What does it mean graphically when the graph of a rational inequality is above the x-axis?

• The inequality is undefined

• The inequality is greater than zero

• The inequality is equal to zero

• The inequality is less than zero

What is the significance of a vertical asymptote in the graph of a rational inequality?

• It indicates a point of intersection

• It indicates a solution to the inequality

• It indicates a zero of the denominator

• It indicates a zero of the numerator

How can a graphing calculator be used to verify the solution of a rational inequality?

• By checking when the graph is tangent to the x-axis

• By checking when the graph intersects the y-axis

• By checking when the graph is above the x-axis

• By checking when the graph is below the x-axis