Rational Inequalities and Interval Notation

The video tutorial explains how to solve a rational inequality by factoring the numerator and denominator, finding zeros, and plotting them on a number line. It then tests intervals to determine which are part of the solution, and finally expresses the solution using inequalities and interval notation.

What is the first step in solving a rational inequality?

• Writing the solution in interval notation

• Graphing the inequality

• Factoring the numerator and denominator

• Testing values on a number line

Which of the following is a zero of the numerator in the given inequality?

• x = 9

• x = -4

• x = 3

• x = 0

How are the zeros of the denominator represented on the number line?

• As open points

• As closed points

• As shaded regions

• As arrows

What is the purpose of testing intervals on the number line?

• To check if the entire interval is part of the solution

• To determine the sign of the expression

• To find the midpoint of the intervals

• To calculate the exact solution

Which test value is used to check the interval to the left of x = -4?

• x = -10

• x = 4

• x = -5

• x = 0

What is the result of the test when x = 0?

• The interval is partially true

• The interval is undefined

• The interval is true

• The interval is false

Why is the interval where x > 3 not part of the solution?

• Because the test value is true

• Because it is not tested

• Because the test value is false

• Because it includes division by zero

How is the solution expressed using inequalities?

• x ≥ 9 or x < -4 and x > 3

• x < 9 or x ≥ -4 and x < 3

• x ≤ 9 or x > -4 and x ≤ 3

• x > 9 or x ≤ -4 and x > 3

What notation is used to express the solution in interval form?

• Interval notation

• Graphical notation

• Set notation

• Algebraic notation

Which interval is closed in the final solution?

• From -∞ to -4

• From 3 to 9

• From -4 to 3

• From 9 to ∞