Rational Inequalities and Their Solutions

The video tutorial explains how to solve rational inequalities algebraically. It begins by identifying the limited domain by setting the denominator equal to zero. Next, it solves the related equation by changing the inequality to an equation and using cross-multiplication. Critical values are identified and placed on a number line. The tutorial then tests intervals to determine which satisfy the inequality. Finally, the solution is expressed in interval notation, covering all values except those that make the denominator zero.

What is the first step in solving a rational inequality algebraically?

• Find the critical values

• Solve the related equation

• Determine the limited domain

• Test the intervals

Why is it important to find the limited domain in rational inequalities?

• To find the maximum value

• To simplify the equation

• To avoid division by zero

• To determine the range of the function

How do you solve the related equation in a rational inequality?

• By adding the numerators

• By setting the inequality to zero

• By cross-multiplying the terms

• By dividing the denominators

What are critical values in the context of rational inequalities?

• Solutions to the related equation and limited domain

• Values that make the denominator zero

• Values that make the numerator zero

• Values that maximize the function

How do you represent a value that is not included in the solution on a number line?

• With a closed circle

• With a shaded region

• With an open circle

• With a dashed line

What is the purpose of testing intervals in solving rational inequalities?

• To determine which regions satisfy the inequality

• To find the maximum value

• To simplify the equation

• To find the critical points

Which value would you test for the interval to the left of -5?

• -6

• 0

• -4

• 3

What does it mean if a test value satisfies the inequality?

• The test value is incorrect

• The entire interval is part of the solution

• The interval is excluded from the solution

• The inequality is invalid

How is the solution to a rational inequality expressed?

• In interval notation

• As a fraction

• As a single number

• In decimal form

What symbol is used in interval notation to indicate that a value is not included?

• Angle bracket

• Square bracket

• Parenthesis

• Curly brace