Inequalities and Interval Notation

The video tutorial explains how to solve inequalities involving fractions by multiplying through by the least common multiple (LCM) of the denominators. It discusses the importance of determining the sign of the multiplier to decide whether to switch the inequality direction. The tutorial then demonstrates solving the inequality and expressing the solution in set and interval notations.

What is the initial inequality presented in the video?

• Zero is less than five over X is less than nine-sevenths

• Zero is greater than five over X is greater than nine-sevenths

• Zero is less than X is less than nine-sevenths

• Zero is greater than X is greater than nine-sevenths

Why do we multiply by the least common multiple (LCM) in the inequality?

• To eliminate fractions

• To add fractions

• To subtract fractions

• To divide fractions

What is the least common multiple (LCM) used in the video?

• 7x

• 3x

• 5x

• 9x

What must be considered when multiplying an inequality by a number?

• The color of the number

• The size of the number

• The shape of the number

• Whether the number is positive or negative

What is the significance of the inequality five divided by X being greater than zero?

• It implies X is undefined

• It implies X is zero

• It implies X is negative

• It implies X is positive

What conclusion is drawn about the sign of X?

• X is undefined

• X is positive

• X is negative

• X is zero

What happens to the inequality when multiplied by the LCM?

• The inequality becomes an equation

• The direction of the inequality reverses

• The direction of the inequality remains the same

• The inequality disappears

What part of the inequality is discarded after simplification?

• Zero is less than 35

• 35 is less than 9x

• Zero is less than X

• X is less than 9

What does the inequality zero is less than 35 imply?

• It is a new discovery

• It is incorrect

• It is a known fact and not useful for solving X

• It is the solution for X

What is the final inequality for X after simplification?

• X is not equal to 35/9

• X is greater than 35/9

• X is less than 35/9

• X is equal to 35/9