Rational Inequalities and Graphical Solutions

The video tutorial explains how to solve rational inequalities by first comparing them to zero, finding a common denominator, and simplifying the expression. It then covers factoring the numerator and denominator, finding zeros, and testing intervals on a number line. The tutorial also demonstrates how to verify solutions graphically, showing that graphical methods can simplify the process.

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

• Divide both sides by a constant

• Multiply both sides by a variable

• Subtract a term to compare to zero

• Add a constant to both sides

Why do we need a common denominator when combining fractions?

• To eliminate the fractions

• To make the inequality positive

• To simplify the numerator

• To ensure the fractions can be added or subtracted

What is the greatest common factor used for in factoring the numerator?

• To change the inequality sign

• To factor out common terms in the numerator

• To find the zeros of the denominator

• To simplify the denominator

What do open points on a number line indicate in the context of rational inequalities?

• Points where the inequality is zero

• Values included in the solution

• Points where the inequality is undefined

• Values excluded from the solution

Which interval is true when testing x = 1?

• The interval is zero

• The interval is false

• The interval is undefined

• The interval is true

What is the result when x = 3 is tested in the inequality?

• The interval is true

• The interval is zero

• The interval is false

• The interval is undefined

How is the solution expressed using interval notation?

• Mixed intervals

• Open intervals

• Single interval

• Closed intervals

What is the advantage of solving the inequality graphically?

• It requires more algebra

• It is less accurate

• It provides a different solution

• It involves less work

When is the graph of the function below the x-axis?

• When x is greater than 0

• When x is between 0 and 2, and greater than 5

• When x is less than 0

• When x is between 2 and 5

What does the graphical method help verify?

• The inequality sign

• The common denominator

• The factorization

• The algebraic solution