Graphing Inequalities and Number Lines

This video tutorial covers solving inequalities on both the number line and the coordinate plane. It explains the use of open and closed circles to represent excluded and included values, respectively. The tutorial demonstrates how to graph inequalities using vertical and horizontal lines, and how to determine the direction of shading. It also discusses the difference between 'and' and 'or' statements in inequalities, providing examples and correcting mistakes to enhance understanding.

What does an open circle on a number line represent?

• The number is included in the solution.

• The number is both included and excluded.

• The number is excluded from the solution.

• The number is irrelevant to the solution.

When graphing x > -2 on the coordinate plane, what type of line should be used?

• Horizontal solid line

• Vertical solid line

• Horizontal dotted line

• Vertical dotted line

How do you indicate that a number is included in the solution on a number line?

• Using a dotted line

• Using a shaded circle

• Using an open circle

• Using a solid line

What type of line is used for inequalities with 'greater than or equal to'?

• Dashed line

• Wavy line

• Solid line

• Dotted line

In the context of graphing inequalities, what does the 'N' symbol indicate?

• Inequalities pointing away from each other

• Inequalities pointing towards each other

• Inequalities that are equal

• Inequalities that are not equal

When graphing y ≥ 4, where should the shading be applied?

• To the right of the line

• To the left of the line

• Above the line

• Below the line

What is the correct shading direction for an 'or' statement in inequalities?

• Only below the line

• Only above the line

• Away from each other

• Towards each other

For the inequality x ≥ -2, what type of line and shading direction should be used?

• Solid line, shading to the left

• Dotted line, shading to the right

• Solid line, shading to the right

• Dotted line, shading to the left

What is the key difference between 'or' and 'and' statements in inequalities?

• 'Or' statements require both conditions to be true.

• 'And' statements require both conditions to be true.

• 'And' statements require only one condition to be true.

• 'Or' statements require only one condition to be true.

In the final example, what was the mistake identified in the video?

• Incorrect number placement

• Incorrect shading direction

• Incorrect line type used

• Incorrect inequality symbol