Graphing Linear Inequalities

The video tutorial explains how to graph linear inequalities on a number line. It covers the format of inequalities, the significance of inequality signs, and how to represent them with open or solid circles and directional arrows. The tutorial emphasizes the importance of having the variable on the left side and provides a method to switch sides if necessary. An example is given to illustrate graphing an inequality, showing how to determine the solution set on the number line.

What is the first step in graphing a linear inequality on a number line?

• Determine the direction of the arrow

• Draw the number line

• Identify the variable and number

• Place the variable on the right

In the preferred format for inequalities, where should the variable be placed?

• On the right-hand side

• On the left-hand side

• In the middle

• Above the number line

What type of circle is used for a 'less than' inequality?

• No circle

• Dashed circle

• Open circle

• Solid circle

How do you graph a 'greater than' inequality on a number line?

• Solid circle, arrow to the left

• Open circle, arrow to the right

• Solid circle, arrow to the right

• Open circle, arrow to the left

How do you graph a 'less than or equal to' inequality?

• Open circle, arrow to the right

• Solid circle, arrow to the left

• Solid circle, arrow to the right

• Open circle, arrow to the left

What does a solid circle on the number line indicate?

• The number is a boundary

• The number is the only solution

• The number is not included in the solution

• The number is included in the solution

What is the requirement for the variable in a linear inequality?

• It must be on the right-hand side

• It must be in the middle

• It must be on the left-hand side

• It can be anywhere

If the variable is on the right, what must you do?

• Switch the variable to the middle

• Leave it as is

• Switch the variable to the left and reverse the inequality sign

• Switch the variable to the left without changing the sign

What happens if the inequality sign is reversed?

• The variable position changes

• The circle type changes

• The arrow direction changes

• The graph remains unchanged

In the example given, what is the position of -3 on the number line?

• Above 0

• To the left of 0

• In the middle

• To the right of 0