Exploring Adding and Subtracting Rational Expressions

This video tutorial introduces algebra students to compound inequalities, focusing on 'or' and 'and' statements. It explains how to graph these inequalities on a number line, highlighting the union and intersection of sets. The tutorial also covers special cases where no solutions exist and provides step-by-step methods for solving compound inequalities. Students learn to identify solutions graphically and algebraically, ensuring a comprehensive understanding of the topic.

What is another term for an 'or' statement in compound inequalities?

• Difference

• Union

• Intersection

• Product

How do you graph x < -1?

• Filled circle at -1, arrow to the right

• Open circle at -1, arrow to the left

• Filled circle at -1, arrow to the left

• Open circle at -1, arrow to the right

In an 'or' statement, what does the graph of x ≥ 2 look like?

• Open circle at 2, arrow to the left

• Filled circle at 2, arrow to the right

• Open circle at 2, arrow to the right

• Filled circle at 2, arrow to the left

What does the word 'and' mean in compound inequalities?

• Union

• Difference

• Intersection

• Product

How do you graph x > -2 and x < 4?

• Open circle at -2, arrow to the right; open circle at 4, arrow to the left

• Filled circle at -2, arrow to the right; filled circle at 4, arrow to the right

• Filled circle at -2, arrow to the right; open circle at 4, arrow to the left

• Open circle at -2, arrow to the left; open circle at 4, arrow to the right

What symbol represents no solution in compound inequalities?

• ∩

• ∅

• ∞

• ∪

What does it mean if a compound inequality has infinite solutions?

• Any real number satisfies the inequality

• There is no overlap between the graphs

• Only one specific number satisfies the inequality

• The inequality has no solution

When solving the inequality 2x < 6, what is the solution for x?

• x > 3

• x ≥ 3

• x < 3

• x ≤ 3

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

• Subtract the same number from both sides

• Flip the inequality sign

• Add the same number to both sides

• Keep the inequality sign the same

How do you graph the solution to the inequality y > 7?

• Open circle at 7, arrow to the left

• Open circle at 7, arrow to the right

• Filled circle at 7, arrow to the right

• Filled circle at 7, arrow to the left