Understanding Inequalities and Interval Notation

The video tutorial explains how to solve and graph inequalities, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It provides two examples: one involving division and the other multiplication, demonstrating how to express solutions using interval notation. The tutorial also covers graphing solutions on a number line, highlighting open and closed intervals.

What must you remember to do when multiplying or dividing both sides of an inequality by a negative number?

• Reverse the inequality symbol

• Keep the inequality symbol the same

• Add a constant to both sides

• Subtract a constant from both sides

In the first example, what operation is used to isolate the variable x?

• Multiplication

• Subtraction

• Addition

• Division

How is the solution to the first inequality expressed on a number line?

• A closed point on -6 with an arrow to the right

• An open point on -6 with an arrow to the left

• A closed point on -6 with an arrow to the left

• An open point on -6 with an arrow to the right

What is the interval notation for the solution of the first inequality?

• (-6, infinity)

• (-infinity, -6]

• (-infinity, -6)

• [-6, infinity)

In the second example, what is the reciprocal of 2/3 used to solve the inequality?

• 3/2

• 3/4

• 2/3

• 1/2

What is the solution to the second inequality in terms of x?

• x is greater than or equal to 6

• x is less than or equal to 6

• x is greater than 6

• x is less than 6

How is the solution to the second inequality represented on a number line?

• An open point on 6 with an arrow to the right

• A closed point on 6 with an arrow to the left

• An open point on 6 with an arrow to the left

• A closed point on 6 with an arrow to the right

What is the interval notation for the solution of the second inequality?

• [6, infinity)

• (-infinity, 6)

• (6, infinity)

• (-infinity, 6]

Which of the following is NOT a way to express the solution of an inequality?

• As a fraction

• As a graph

• Using interval notation

• As an inequality

What does a rounded parenthesis in interval notation indicate?

• The interval is closed

• The interval includes the endpoint

• The interval is infinite

• The interval is open