Rational Inequalities and Intervals

The video tutorial explains how to solve a rational inequality by determining the zeros of the numerator and denominator, plotting these zeros on a number line, and testing intervals to find the solution. The solution is expressed using both inequalities and interval notation, and the process is visualized on a number line.

What is the first step in solving a rational inequality?

• Factoring the numerator and denominator

• Stating the solution in interval notation

• Graphing the solution

• Finding the test values

What are the zeros of the numerator and denominator used for?

• To determine the intervals on the number line

• To find the test values

• To solve the inequality directly

• To graph the solution

Why are zeros of the denominator represented as open points on the number line?

• Because they are part of the solution

• Because they indicate a test value

• Because division by zero is undefined

• Because they are always positive

How many sub-intervals are created on the number line after plotting the zeros?

• Five

• Four

• Three

• Two

What is the purpose of selecting test values in each sub-interval?

• To check if the entire interval satisfies the inequality

• To factor the expression

• To graph the solution

• To determine the zeros

Which test value indicates that the interval from -4 to 0 is part of the solution?

• X = -1

• X = 1

• X = -5

• X = 0

What does a false test value indicate about an interval?

• The interval is part of the solution

• The interval is always positive

• The interval needs to be re-evaluated

• The interval is not part of the solution

What is the solution to the inequality in interval notation?

• (-∞, 0]

• (-∞, -4]

• (-4, 0]

• [0, ∞)

How is the solution expressed using a compound inequality?

• X < -4 or X > 0

• X < 0 or X > -4

• X ≤ -4 and X ≥ 0

• X > -4 and X ≤ 0

What symbol is used to indicate that -4 is not included in the solution interval?

• Angle bracket

• Square bracket

• Curly brace

• Parenthesis