Exploring Inequalities in Algebra

What does a filled boundary point on a number line indicate?

• Includes the boundary value

• Excludes the boundary value

• None of the above

• Indicates a multiplication

If an inequality has a boundary point that is open, what does it signify?

• The boundary value is included

• The boundary value is not included

• The value is multiplied

• The value is undefined

Which of the following is a method to graph an inequality that includes the boundary?

• None of the above

• Using an open circle on the number line

• Drawing a square at the boundary

• Using a filled circle on the number line

How do you solve an inequality where the variable is multiplied by a negative number?

• Keep the inequality sign the same

• Flip the inequality sign

• Add the number to both sides

• None of the above

In the context of inequalities, what does 'solving' refer to?

• Graphing on a number line

• Isolating the variable on one side

• Finding the maximum value

• None of the above

What is the correct graphical representation for x > -3?

• Arrow pointing left from -3

• Arrow pointing right from 3

• Arrow pointing right from -3

• Arrow pointing left from 3

What happens to the inequality sign when you divide both sides by a negative number?

• It disappears

• It doubles in value

• It flips to the opposite direction

• It remains unchanged

What is indicated by an arrow pointing to the left on a number line in the context of inequalities?

• Values greater than the boundary

• Values less than the boundary

• Values equal to the boundary

• None of the above

When solving x/(-3) < 4, what is the first step?

• Multiply both sides by -3 and flip the inequality

• Divide both sides by -3

• Subtract 4 from both sides

• Add 3 to both sides

How do you handle an inequality with a fraction like x/2 < 4?

• Multiply both sides by 2

• None of the above

• Subtract 2 from both sides

• Divide both sides by 2