Domain with radicals in numerator and denominator

The video tutorial explains how to handle and solve inequalities with constraints. It covers the process of identifying constraints, solving inequalities, and graphing solutions on a number line. The tutorial emphasizes the importance of ensuring solutions satisfy all constraints and demonstrates how to determine the domain where all conditions are met.

What is the first step when solving an inequality that involves flipping the sign?

• Multiply both sides by a positive number

• Divide both sides by a negative number

• Add the same number to both sides

• Subtract the same number from both sides

Which of the following represents the solution for X in the inequality X < 1/3?

• X is not equal to 1/3

• X is greater than 1/3

• X is less than 1/3

• X is equal to 1/3

When plotting the inequality X > -1/3 on a number line, what type of circle is used at -1/3?

• Closed circle

• Open circle

• Half-filled circle

• No circle

What is the domain of the solution when both inequalities X < 1/3 and X > -1/3 are true?

• (-1/3, ∞)

• [1/3, -1/3]

• (-∞, 1/3)

• (-1/3, 1/3)

Why is it important to consider both inequalities when determining the domain?

• Because it eliminates the need for a number line

• Because the domain is only valid if both conditions are met

• Because one inequality is always false

• Because it simplifies the solution