Solving Algebraic Inequalities: Key Concepts and Techniques

Professor Dave explains inequalities in algebra, contrasting them with equations. He demonstrates solving simple inequalities and representing solutions on a number line. The video also covers handling inequalities with negative numbers, emphasizing the need to flip the inequality sign when multiplying or dividing by a negative number.

What does an inequality in algebra indicate about the relationship between two terms?

• None of the above

• They are multiples of each other

• One is greater or less than the other

• They are equal

How is a value that is not included in the solution of an inequality represented on a number line?

• With a triangle

• With a square

• With an open circle

• With a closed circle

What happens to the inequality 'X > 3' if X is replaced with 3.00001?

• It becomes an equation

• It becomes false

• It is undefined

• It remains true

If 'X + 2 < 7', what is the solution for X?

• X < 9

• X < 7

• X < 5

• X < 3

If 'X is less than five', which of the following values is not a solution?

• 2

• 3

• 4

• 5

What does the symbol '≥' signify in an inequality?

• Greater than

• Less than

• Less than or equal to

• Greater than or equal to

Which of the following is a correct representation of an inequality where the value is included in the solution?

• A solid line without endpoints

• Open circle on the number line

• Closed circle on the number line

• A dotted line

What is the solution for the inequality '3X + 4 ≥ 16'?

• X ≥ 4

• X ≥ 6

• X ≤ 6

• X ≤ 4

What must be done to the inequality symbol when multiplying or dividing both sides by a negative number?

• It is removed

• It becomes an equation

• It remains the same

• It must be reversed

Why do we reverse the inequality symbol when dividing by a negative number?

• To simplify the inequality

• None of the above

• Because it's a mathematical error to not do so

• To maintain the logical order of numbers