Rational Inequalities and Critical Points

This video tutorial by Premath provides a step-by-step guide to solving and graphing a rational inequality. It begins with setting up the inequality by ensuring zero is on one side. The tutorial then simplifies the inequality using cross-multiplication and identifies critical values by setting the numerator and denominator to zero. It tests these critical points on a number line to determine valid regions. The video concludes by identifying the solution in interval notation and provides a graphical representation.

What is the first step in solving a rational inequality?

• Move all terms to the right-hand side

• Ensure that one side of the inequality is zero

• Add 5 to both sides

• Multiply both sides by the denominator

How can the number 5 be written to facilitate simplification?

• As 5x

• As 5 over 2

• As 5 over 1

• As 1 over 5

What method is used to combine the two fractions in the inequality?

• Addition

• Subtraction

• Cross multiplication

• Division

What are the critical points found by setting the numerator and denominator to zero?

• x = 3 and x = 4

• x = 0 and x = 5

• x = 1 and x = 2

• x = 2 and x = 3

What happens when x = 3 is substituted into the inequality?

• The inequality equals zero

• The inequality is true

• The inequality is false

• The inequality becomes undefined

What is the result when x = 2 is substituted into the inequality?

• The inequality is false

• The inequality equals zero

• The inequality becomes undefined

• The inequality is true

Which region is ruled out after testing x = 0?

• Region C

• Region A

• Region D

• Region B

What is the result when x = 2.5 is substituted into the inequality?

• The inequality equals zero

• The inequality is true

• The inequality is false

• The inequality becomes undefined

What is the result when x = 4 is substituted into the inequality?

• The inequality is true

• The inequality equals zero

• The inequality is false

• The inequality becomes undefined

What is the final solution in interval notation?

• (2, 3)

• [2, 3)

• (2, 3]

• [2, 3]