Understanding Interval Notation and Inequalities

The video tutorial explains how to solve a rational inequality and express the solution using interval notation. It begins by rewriting the inequality as a quotient and finding a common denominator. The process involves simplifying the inequality, determining the zeros of the numerator and denominator, and plotting these on a number line. The tutorial then tests different intervals to verify which satisfy the inequality, concluding with expressing the solution in interval notation.

What is the first step in solving a rational inequality?

• Add a constant to both sides

• Multiply both sides by a variable

• Divide both sides by a constant

• Rewrite the inequality as a quotient on the left and zero on the right

How do you simplify the inequality after rewriting it?

• By adding a constant to the numerator

• By multiplying the numerator by a variable

• By finding a common denominator

• By subtracting a constant from the denominator

What is the next step after simplifying the inequality?

• Rewrite the inequality as a product

• Multiply both sides by a variable

• Add a constant to both sides

• Determine the zeros of the numerator and denominator

How is the zero of the denominator plotted on the number line?

• As a solid line

• As a dashed line

• As an open point

• As a closed point

What is the purpose of testing intervals in solving inequalities?

• To find the exact solution

• To determine which intervals satisfy the inequality

• To simplify the inequality further

• To eliminate unnecessary terms

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

• x = 0

• x = 4

• x = 5

• x = 41/9

What is the result when a positive numerator is divided by a negative denominator?

• Positive

• Zero

• Negative

• Undefined

How is the solution expressed using interval notation?

• Using algebraic expressions

• Using open and closed intervals

• Using a number line

• Using inequalities

What type of bracket is used for a closed interval?

• Angle bracket

• Round bracket

• Square bracket

• Curly bracket

What does the interval from negative infinity to positive four represent?

• All values between four and infinity

• All values less than four

• All values greater than four

• All values between zero and four