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: solving 5x > -25 and -4x ≥ -20, demonstrating how to express solutions using interval notation and graphing on a number line.

What must you do to the inequality symbol when you multiply or divide both sides of an inequality by a negative number?

• Leave it unchanged

• Add a positive number to both sides

• Subtract a positive number from both sides

• Reverse it

Why is it necessary to reverse the inequality symbol when dividing by a negative number?

• To make the inequality false

• To ensure the inequality remains true

• To simplify the equation

• To eliminate negative numbers

In the example where 5x > -25, what is the solution for x?

• x < -5

• x ≤ -5

• x > -5

• x = -5

How is the solution for 5x > -25 expressed in interval notation?

• (-∞, -5)

• [-5, ∞)

• (-5, ∞)

• (-∞, -5]

What does an open point on a graph indicate about a number in an interval?

• The number is not included in the interval

• The number is included in the interval

• The number is the midpoint of the interval

• The number is the endpoint of the interval

In the example -4x ≥ -20, what operation is performed to solve for x?

• Add 20

• Multiply by 4

• Subtract 20

• Divide by -4

What is the solution for x in the inequality -4x ≥ -20?

• x ≤ 5

• x > 5

• x ≥ 5

• x < 5

How is the solution for -4x ≥ -20 expressed in interval notation?

• (5, ∞)

• (-∞, 5]

• [5, ∞)

• (-∞, 5)

What type of bracket is used in interval notation to indicate that a number is included in the interval?

• Angle bracket

• Curly bracket

• Square bracket

• Rounded parenthesis

What is the significance of using a rounded parenthesis in interval notation?

• It indicates the interval is closed

• It indicates the interval is finite

• It indicates the interval is open

• It indicates the interval is infinite