Testing Intervals in Rational Inequalities

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

What is the first step in solving a rational inequality?

• Testing intervals

• Factoring the numerator and denominator

• Graphing the solution on a number line

• Expressing the solution using interval notation

How do you find the zeros of the numerator?

• By setting the numerator equal to zero and solving for x

• By setting the denominator equal to zero and solving for x

• By graphing the numerator

• By testing intervals

What type of point is used for the zero of the denominator on the number line?

• Solid point

• Closed point

• Dashed point

• Open point

Why is a closed point used for the zero of the numerator in this case?

• Because the inequality is strict

• Because the inequality includes 'greater than or equal to'

• Because the numerator is zero

• Because the denominator is zero

What is the purpose of testing intervals in solving rational inequalities?

• To find the zeros of the numerator

• To determine if the entire interval satisfies the inequality

• To factor the denominator

• To express the solution using inequalities

Which test value is used to check the interval on the left?

• x = 6

• x = 0

• x = -7

• x = 8

What is the result of testing x = 0 in the middle interval?

• The interval is false

• The interval is undefined

• The interval is true

• The interval is partially true

What does the graph of the solution indicate about the intervals?

• All intervals are part of the solution

• Only the left and right intervals are part of the solution

• None of the intervals are part of the solution

• Only the middle interval is part of the solution

How is the solution expressed using inequalities?

• x < -7 or x ≥ 5

• x < -7 or x > 5

• x ≤ -7 or x ≥ 5

• x ≤ -7 or x > 5

What interval notation represents the solution?

• (-∞, -7] ∪ (5, ∞)

• (-∞, -7) ∪ [5, ∞)

• (-∞, -7] ∪ [5, ∞)

• (-∞, -7) ∪ (5, ∞)