Rational Inequalities and Equations

This video tutorial covers Module 6, focusing on solving rational equations and inequalities. It explains key concepts such as inequalities, extraneous solutions, and the use of least common denominators (LCD) in solving equations. The tutorial also discusses properties of equality, methods to verify solutions, and how to express solution sets in interval notation. Additionally, it provides a step-by-step guide to solving rational inequalities and testing solutions.

What is the first step in solving rational equations and inequalities?

• Ignore the instructions.

• Choose the best answer from given options.

• Write the answer on the same sheet.

• Solve without understanding.

Which of the following best describes an inequality between two expressions?

• A rational equation.

• An algebraic equation.

• A complex equation.

• A simple equation.

What is an extraneous solution?

• A solution that is always incorrect.

• A solution that seems correct but is not.

• A correct solution.

• A solution that is always correct.

What is the usual technique to solve rational equations?

• Divide both sides by the least common denominator.

• Multiply both sides by the least common denominator.

• Subtract both sides.

• Add both sides.

What is the least common denominator (LCD) of 3, 4, and 2?

• 10

• 6

• 8

• 12

Which property is used when multiplying the LCD on both sides of an equation?

• Subtraction property of equality.

• Addition property of equality.

• Division property of equality.

• Multiplication property of equality.

After applying the multiplication property, what is the next step?

• Apply the addition property.

• Apply the distributive property.

• Apply the division property.

• Apply the subtraction property.

How can you verify if your solution to a rational equation is correct?

• By guessing.

• By substituting the solution back into the original equation.

• By checking with a calculator.

• By asking a friend.

What should you do if a solution makes an expression undefined?

• Use the solution anyway.

• Ignore the solution.

• Accept the solution.

• Reject the solution.

Which of the following is not an inequality sign?

• ≤

• >

• √

• <