Solving Rational Inequalities Concepts

This video tutorial covers rational inequalities, explaining how to solve them by factoring, determining zeroes, and testing intervals. It includes examples demonstrating the process, both algebraically and graphically, using a graphing calculator. The tutorial also addresses handling inequalities not initially compared to zero, emphasizing the importance of simplifying and factoring.

What is the first step in solving a rational inequality?

• Factor the numerator and denominator

• Graph the inequality

• Multiply both sides by zero

• Add a constant to both sides

When plotting zeroes on a number line, what type of point is used for the zeroes of the denominator?

• Closed point

• Open point

• Solid point

• Dashed point

In the first example, which interval was part of the solution?

• From -3 to 0

• From 0 to 4

• From 3 to 5

• From -2 to 3

What does the graph of a rational function help determine in solving inequalities?

• When the function is decreasing

• When the function is above the x-axis

• When the function is below or on the x-axis

• When the function is increasing

In the second example, what are the zeroes of the numerator?

• x = -1 and x = 1

• x = 1/3 and x = 2

• x = 0 and x = 4

• x = -3 and x = 3

How many intervals need to be tested in the second example?

• 3

• 4

• 5

• 6

What is the purpose of using a graphing calculator in solving rational inequalities?

• To factor the expression

• To find the exact solution

• To evaluate the sign of the expression

• To simplify the expression

What is the graphical representation of a rational inequality solution?

• On the y-axis

• Below or on the x-axis

• Above the x-axis

• Above the y-axis

What must be done if a rational inequality is not compared to zero?

• Divide both sides by a constant

• Multiply both sides by zero

• Subtract the expression from both sides

• Add a constant to both sides

What is the final step after transforming a rational inequality to the correct form?

• Test the intervals

• Simplify the expression

• Factor the numerator

• Graph the inequality