Rational Inequalities and Their Solutions

The video tutorial explains how to solve a rational inequality and express the solution using interval notation. It begins by setting up the inequality as a single quotient and simplifying it by finding a common denominator. The zeros of the numerator and denominator are determined, and these values are plotted on a number line. The tutorial then tests intervals to identify which satisfy the inequality, leading to the final solution expressed in interval notation.

What is the first step in solving the given rational inequality?

• Add 16/19 to both sides

• Multiply both sides by the denominator

• Divide both sides by 3x

• Subtract 16/19 from both sides

What is the least common denominator used in the initial steps?

• 19 * (4x + 1)

• 19

• 4x + 1

• 3x - 1

How is the numerator simplified in the inequality?

• By adding the terms directly

• By dividing each term by 19

• By multiplying and combining like terms

• By subtracting the terms

What is the zero of the numerator in the simplified inequality?

• x = 0

• x = -1/4

• x = -5

• x = 5

What is the zero of the denominator in the simplified inequality?

• x = 0

• x = -1/4

• x = -5

• x = 5

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

• As open points

• As closed points

• As undefined points

• As both open and closed points

Why are the zeros of the denominator always open points?

• Because they are part of the solution

• Because division by zero is undefined

• Because they are greater than zero

• Because they are less than zero

Which test value is used to check the interval to the left of x = -5?

• x = 0

• x = -4

• x = -6

• x = -1

What is the sign of the numerator when x = 0?

• Negative

• Zero

• Undefined

• Positive

What is the interval notation for the solution of the inequality?

• (-∞, -5]

• [-5, -1/4)

• (-5, -1/4]

• [-1/4, ∞)