Rational Inequalities and Intervals

The video tutorial explains how to solve a rational inequality using interval notation. It begins by rewriting the inequality with a common denominator, then finds the zeroes of the numerator and denominator. These zeroes are plotted on a number line to determine open and closed points. The tutorial tests intervals to identify which satisfy the inequality, concluding with the solution expressed in interval notation.

What is the first step in solving a rational inequality?

• Add a constant to both sides

• Subtract a constant from both sides

• Rewrite the inequality with a common denominator

• Multiply both sides by the denominator

How do you simplify the expression 5x - 1 + 3(6x + 7)?

• 5x + 18x + 7

• 18x + 21

• 3x + 6x + 7

• 23x + 20

What is the zero of the numerator 23x + 20?

• x = 7/6

• x = 20/23

• x = -20/23

• x = -7/6

Which point is always open on the number line?

• Zero of the numerator

• Zero of the denominator

• Neither zero

• Both zeros

What test value is used for the interval to the right of -20/23?

• x = -21/23

• x = 0

• x = -2

• x = 1

What is the result when both the numerator and denominator are negative?

• Undefined

• Zero

• Negative

• Positive

Which interval is true when testing x = -21/23?

• Left interval

• Middle interval

• None

• Right interval

How is the solution expressed in interval notation?

• [-7/6, -20/23]

• (-20/23, -7/6)

• (-7/6, -20/23)

• [-20/23, -7/6]

What does an open interval indicate about the endpoints?

• Endpoints are included

• Endpoints are infinite

• Endpoints are zero

• Endpoints are excluded

If the inequality symbol was 'less than or equal to', what would change?

• No change

• The zero of the numerator would be a closed point

• The zero of the denominator would be a closed point

• Both zeros would be closed points