Rational Inequalities and Intervals

The video tutorial explains how to solve rational inequalities by factoring the numerator and denominator, finding zeros, and plotting them on a number line. It demonstrates testing intervals to determine which satisfy the inequality and concludes with graphing the solution and expressing it using inequalities and interval notation.

What is the first step in solving a rational inequality?

• Testing values in intervals

• Finding the zeros of the inequality

• Factoring the numerator and denominator

• Graphing the inequality

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

• Closed point

• Open point

• Solid point

• Dashed point

How many sub-intervals are created when the number line is divided by the zeros?

• Five

• Four

• Three

• Two

Which test value is used to check the interval between -4 and 3?

• x = -5

• x = 4

• x = 0

• x = 9

What is the result when testing x = 4 in the rational inequality?

• True, the interval satisfies the inequality

• The test value is not applicable

• False, the interval does not satisfy the inequality

• The test value is undefined

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

• To check if the entire interval satisfies the inequality

• To factor the numerator and denominator

• To graph the solution

• To determine the zeros of the inequality

What is the correct interval notation for the solution where x is greater than -4 and less than or equal to 3?

• (-4, 3]

• (-4, 3)

• [-4, 3]

• [-4, 3)

Which of the following intervals is part of the solution for x > 8?

• (8, ∞]

• [8, ∞)

• [8, ∞]

• (8, ∞)

What is the inequality representation for the solution where x is greater than -4 and less than or equal to 3?

• x ≤ -4 and x > 3

• x ≥ -4 and x < 3

• x < -4 and x ≥ 3

• x > -4 and x ≤ 3

What type of bracket is used to indicate that a number is included in an interval?

• Angle bracket

• Square bracket

• Curly bracket

• Parenthesis